Unvented water heaters have several components:
Tank
Inlet pressure regulator
Non-return valve
Heater and adjustable thermostat
Backup-thermostat with manual reset (cuts power to heater if main thermostat fails)
Expansion space or reservoir
Pressure relief valve
Temperature and pressure relief valve
Under normal conditions the tank is pressurised by the mains water to the pressure set on the input regulator. As the water heats it expands. The NR valve prevents water in the tank back-tracking into the cold water supply or damaging the regulator.
Normally, an expansion reservoir (e.g. an air bubble at the top of the tank, or a rubber air-filler bladder) takes up the expansion.
However, if the expansion reservoir is unable to absorb the entire expansion (e.g. water too hot, regulation pressure too high, air bubble all dissolved, or bladder damaged) then the pressure will rise, and will cause the pressure relief valve to release water. This water will be a slow trickle, and will only be a gallon or so.
If the pressure valve malfunctions, or if the backup thermostat malfunctions and the water gets too hot, then the temperature and pressure valve will open. While the P valve will open just enough to release the pressure the T&P valve will open full-on when triggered and water will hose out of the tank until the temperature comes down, or the pressure comes down.
The P and T&P valves must be allowed to drain visibly into a metal drain pipe. Visible drainiage is required so that faults can be seen. The metal pipe is required because in the event of an overtemperature fault - near-boiling water (at 205 F) will be released from the T&P valve at full water pressure. This high temperature and flow-rate will melt or weaken plastic pipes, unless specially rated for water heater drainage use.
The reason for 4 seperate fail safes is because of the risk of steam explosion. If steam pressure was allowed to build up until tank rupture; an exploding tank can easily demolish an entire house.
If your tank is of the air bubble expansion type, then replenishing the air bubble may solve the problem. The service manual will have instructions on how to do this - it usually involves draining the tank down a bit, and then manually opening the T&P valve to allow the tank to suck in air.
If the tank is old (over 10 years), and doesn't have dual protection valves, then it would be sensible to replace it, especially as cheap copper tanks have only a relatively short life.