A Layman's description of How ACAS Works -
ACAS is a last ditch collision warning system (when all else fails, i.e. eyeballs, procedures, ATC). It does not take over from the pilot.
It identifies and monitors transponders on other aircraft and displays them in the cockpit for pilots to monitor. It depends on conflicting aircraft having operating transponders that are turned on.
It issues an aural Traffic Advisory (TA) when an intruder is 20-48 seconds away
Issues an aural Resolution Advisory (RA) when intruder is 15-35 seconds away). This tells the pilot to climb or descend in order to resolve a potential collision.
ACAS is not connected to the autopilot-the pilot must take the action to avoid a collision
ACAS can issue an advisory warning or RA, even though a collision may not have occurred, due to the proximity of the other aircraft. However, a TCAS warning is very serious and should be obeyed, even if ATC is involved and giving conflicting instructions.
ACAS is not infallible, unpredictable actions of intruder aircraft, such as military aircraft, can defeat the system.But it's absolutely essential for passenger operations.
ACAS is believed to be about 70% effective at avoiding collisions; 30% is still down to the skill of the pilots and all the other operational rules/procedures (such as level restrictions; ATC intervention etc) that are in place to prevent conflicts. But it's better than the eyeball which is only up to 20% effective, and less so, for high speed and IFR aircraft.