(A320 PTU (Vickers), source)
The Power Transfer Unit is well known on Airbus due to its barking-like sound (refresher: Video of a PTU in action). The sound comes from a pump which creates a 3,000 psi pressure being quickly switched ON and OFF.
The PTU is a safety system to ensure hydraulic pressure is available, specially at takeoff, even if one or two hydraulic circuits have failed.
The PTU can restore pressure in a deficient circuit without actually transferring fluid from the working circuit to the deficient one. This prevents throwing hydraulic fluid from the working circuit overboard if the deficient circuit is leaking.
The PTU is always activated, but is actually triggered based on a pressure differential.
When is it activated?
On Airbus A320 series, the PTU is actually the second source of pressure for the yellow and green hydraulic systems, after the EDP. It's always ON, ready for the pump activation if there is a pressure drop on the yellow or green hydraulic system and the differential pressure is more than 500 psi.
Airbus A318, A319, A320 and A321 aeroplanes are equipped with three
hydraulic systems and they can be safely controlled with only one
system operative. A bi-directional PTU enables the yellow system to
pressurize the green system, and vice versa, without the transfer of
fluid from one system to the other.
In flight, the PTU operates
automatically if a pressure drop in one of the systems is detected.
The PTU ensures optimal hydraulic system availability for take-off.
(Source: EASA safety bulletin)
Automatic inhibition below 1,500 ft in case of leakage
The PTU cannot restore the correct pressure in a circuit with a permanent leak. In this case, the PTU, and possibly the working hydraulic system, eventually overheat. The crew receives a failure amber caution on the ECAM display and, up to recently, had to switch OFF (inhibit) the PTU manually to prevent damage.
In case of loss of hydraulic fluid of the yellow or green system, the PTU
cannot pressurize the failed system and must be switched OFF as
required by ECAM procedure to avoid a PTU overheat which may occur two
(Source: EASA safety bulletin)
A320 PTU switch (source: Baltic Aviation Academy which, by the way, has plenty of quality training videos)
To avoid distraction from non-essential warnings during takeoff and landing, the ECAM message is not displayed when airborne below 1,500 ft height. There were several incidents (e.g. G-EZDM) where overheating became harmful before the amber ECAM message appeared at 1,500 ft, causing the temporary loss of a second system. Airbus added logic for automatic PTU inhibition when the aircraft is airborne, but still below 1,500 ft.
The previous quotes are from an EASA bulletin related to this modification (also detailed in Safety First, the Airbus safety magazine), with a failure scenario that had to be prevented:
A PTU is connected to two independent hydraulic systems: The first to drive an hydraulic motor (or turbine) mechanically connected to a pump. The second hydraulic system is pressurized by the pump.
PTU principle, source
PTU can be reversible (each hydraulic system can drive the motor or be pressurized by the pump) or not (the same system always drive the motor).
(Actual PTU schematics, source)