It took me a while to understand the big picture regarding mechanical ventilation. If you want to have a more professional understanding about this subject, please check references , ,  and . They helped me to understand the puzzle.
Here are some of the most important concepts I researched about mechanical ventilation. I did my best to describe what I learned in the simplest possible way.
Continuous Mandatory Ventilation (CMV)
Continuous Mandatory Ventilation (also called Assisted Control) is a mode of mechanical ventilation in which breaths are delivered based on defined variables. In this mode, the ventilator does 100% of the work, so it is most efficient for patients with complete respiratory failure.
Patients that are sedated, paralyzed, or need to rest will need to be in CMV for proper ventilation. CMV ventilation is delivered to the patient through an endotracheal tube.
Breaths in CMV can be triggered by:
Time: The breath is given at a set time according to the rate of the machine. For example, a rate of 10 breaths a minute means every 6 seconds a breath is initiated by the machine.
Patient: The breath is given whenever flow or negative pressure against the endotracheal tube is detected (patient trying to breath). When the system is designed to be triggered by flow, the threshold is usually set in the range 1 to 4 L/min. When the system is designed to be triggered by negative pressure, the threshold is usually in the range -1 to -5 cm H2O.
It is important to say that, in CMV, the “Patient trigger” always includes “Time trigger” as backup.
CMV provides the assisted breath every time it is triggered (by time or by the patient), according to the parameters set. If the patient begins to actively participate in breathing, this mode will become less effective and could lead to “air trapping” (when the lungs cannot fully expel the air before another breath is initiated).
Synchronized Intermittent Mandatory Ventilation (SIMV)
Different from the CMV, the SIMV is the most common mode of ventilation used for conscious patients who do not require 100% of the work being done for them.
This mode allows patients an opportunity to breath on their own between the set rate of breaths given by the machine. However, if no inspiratory effort is detected by the ventilator, a time triggered breath is delivered. The ventilator waits until the patient exhales before delivering another mechanical breath. This "synchronizes" the ventilator to the spontaneous breathing.
CMV and SIMV can be either Volume Controlled (VC) or Pressure Controlled (PC).
Volume Controlled (VC)
VC is a control method for when a predetermined volume of air is set (constant) on the equipment. Every time the ventilator cycles a breath, the patient receives that volume of air (known as “Tidal Volume”). When this volume setting is reached, the ventilator cycles off and the patient exhales.
There are two main benefits of VC. The first is the fact the technique is widely known and understood, and the second being the controllable air flow (known as “Minute Volume”).
The concern of VC is that the constant flow may cause high peak pressures, thus exposing the patient to the risk of barotraumas.
(In my opinion, this control method should be called "Flow Controlled" instead of "Volume Controlled")
Pressure Controlled (PC)
PC is when a predetermined pressure limit is set on the equipment. Every time the ventilator cycles a breath, the pressure will continue to rise on the ventilator until the pre-set pressure limit is reached. When the pressure limit setting is reached, the ventilator will then cycle off and the patient will exhale.
The amount of air volume the patient will receive (Tidal Volume) depends on how high the pressure limit is set.
The advantage of PC over VC is to provide a better protection to the lungs, causing less risk of barotraumas.
However, if the lungs are too stiff (“low compliance”) the desired tidal volume will not be delivered because the pressure will rise fast during the inspiration. Therefore, the disadvantage of PC is that the tidal volume will change according to lung compliance, so a desired air supply may not be guaranteed.
Pressure Regulated Volume Controlled (PRVC)
To address the problem mentioned in the last paragraph above, the PRVC was created.
In PRVC (also called PCV-VG), a preset tidal volume is delivered to the patient while maintaining the lowest pressure possible in the airway by using a decelerating flow to avoid “barotrauma”.
This is a mode that provides the benefits of variable flow from PC along with the “guaranteed” air delivered of VC.
In other words, in PRVC, the ventilator uses a feedback method on a breath-to-breath basis to continuously adjust the pressure delivered to achieve the tidal volume target.
Pressure Support Ventilation (PSV)
Another ventilation mode, in addition to CMV and SIMV, is PSV, which is used only to increase spontaneous breathing.
In PSV, the patient initiates every breath and the ventilator delivers support with the preset pressure value. With support from the ventilator, the patient also regulates their own respiratory rate, air flow, and tidal volume (but not pressure, as this is pressure-controlled).
In other words, PSV allows the patient to determine tidal volume, respiratory frequency, and flow (but again, not pressure, as the system is pressure-controlled).
With some ventilators, there is the ability to set a back-up SIMV in case spontaneous respiration cease (at least an alarm is necessary!).
PSV is frequently the mode of choice in patients whose respiratory failure is not severe and who have an adequate respiratory drive. PSV can be delivered through specialized face masks instead of endotracheal tubes.
Several data indicate that PSV may be safely and successfully used during the early phase of acute respiratory failure in most Acute Respiratory Distress Syndrome (ARDS) patients 
Figure 1 presents an overview of these ventilation modes and respective control methods.
Figure 1 - Overview of some ventilation modes and control methods
Parameters & Variables
The following basic parameters and variables are the ones that I found most used in the ventilation science.
Tidal Volume (TV)
This is the volume of air set to be delivered with each breath.
In case an ambu bag is used, the tidal volume is the volume of air that leaves the ambu bag every time it is pressed.
In an arrangement where an ambu bag is pressed by a linear actuator, the tidal volume is a function of the actuator displacement.
In ARDS, Tidal Volume is calculated by multiplying the patient’s mass (in kilograms) by a factor ranging from 4 to 8 mL/kg.
Respiratory Rate (RR)
This is how many breaths per minute are delivered to the patient.
In ARDS, this frequency varies from 8 to 40 BPM (breaths per minute).
Inspiratory Time (IT)
This is the time spent during the inspiratory phase (also called “triggering” phase).
Expiratory Time (ET)
This is the time spent during the expiratory phase (also called “cycling” phase).
Inspiratory/Expiratory Ratio (I:E)
This is the relation between the Inspiratory Time (IT) and Expiratory Time (ET).
It normally varies from 1:1 to 1:3, but in Acute Respiratory Distress Syndrome (ARDS), patients usually go up to 1:4.
Example: I:E = 1:2 and RR = 10 BPM:
A patient with a rate of 10 breaths per minute would be allowed 6 seconds for a cycled breath.
In this case, the cycle will contain 2 seconds for inspiration (IT) and 4 seconds for expiration (ET).
Minute Ventilation (MV)
This is the amount of air delivered per minute to the patient (flow).
The goal is to keep Minute Ventilation in the range 5 – 10 L/min.
In an ideal world, the Minute Ventilation is equal to the Tidal Volume times the Respiratory Rate:
(MV = TV * RR).
Peak Inspiratory Pressure (PIP)
This is the maximum pressure that can be reached during an inspiration.
A typical ambu bag normally comes with a “pop-off” valve to protect the patient against a peak inspiratory pressure.
Pop-off valves in ambu bags usually open in the 40 to 80 cmH2O range, depending on the ambu bag brand.
Plateau Pressure (Pplat)
Plateau pressure is the pressure within the breathing circuit following an end-inspiratory pause, which allows equalization of any pressure difference between the alveoli and the circuit.
Most ventilators have the capability to perform this “end-inspiratory hold” for a configurable duration. This hold is normally set between 0.5 and 1 second.
In other words, the Plateu Pressure is a threshold, and it is normally set between 40 and 60 cm H2O. For Acute Respiratory Distress Syndrome (ARDS), analysis demonstrates lower mortality rate when using Plateu Pressure <= 40 cm H2O .
Positive End Inspiratory Pressure (PEEP)
This is the pressure that remains in the airways at the end of the respiratory cycle.
It is applied to maintain an ‘open lung’, preventing alveolar collapse and thus improving gas exchange and minimizing atelectrauma.
A PEEP valve is used over the exhaled air to keep that pressure in a positive constant value (5 – 20 cm H2O).
Lung Compliance (C')
Lung compliance is a measure of the lung's ability to stretch and expand (distensibility of elastic tissue).
Low compliance indicates a stiff lung (one with high elastic recoil) and can be thought of as a thick balloon (e.g.: fibrosis).
High compliance indicates a pliable lung (one with low elastic recoil) and can be thought of as a grocery bag (e.g.: emphysema).
Pulmonary compliance is calculated using the following equation: Compliance = ΔV/ΔP, where ΔV is the change in volume, and ΔP is the change in pleural pressure.
Fraction of Inspired Oxygen (FiO2)
This is the percentage of oxygen in the air mixture given to the patient.
Room air has FiO2 of approximately 21%. Whenever oxygen supply is added to the ventilation cycle, it normally ranges from 30-100%.
Ambu bags typically have a port to connect to oxygen supply.