Tartare,
To add to Engines reply, water injection sprayed de-mineralised water, at pressure, onto the HP turbine blades and reduced the Jet Pipe Temp (JPT) by 23-25C. This temperature suppression allows increased fuel flow (and therefore RPM under certain conditions). The net effect of higher RPM and increased mass flow is more thrust - Harrier only had 90 sec of aggregate water flow.
The 'wet' and dry engine lifts were governed by a number of factors such as water switch position and gear/PLAU positions, not by the contents of the water tank. You could be in a position where you might be operating the engine to the higher 'wet' limits but if you didn't have water (I.e. you had run out) you would be fatiguing the engine per second like billy-oh. Hence, there was some (but not necessarily crucial) priority to get the jet landed before the water was gone.
Importantly, you didn't always need water to hover (low ambient temp, high atmospheric pressure), but if you did - and ran out mid-hover - there were fortunately only a few conditions where you would actually descend whilst at max throttle position.