The pressure relief valve on a hot-water tank is meant to relieve pressure to prevent damage to the tank. It is needed for a few reasons, e.g.,
- The water tank holds a large volume of water. If the water inside actually boils (e.g., a thermostatic switch fails), it might explode if there were no relief valve.
- There can be pressure surges in a water main and the valve would open before the (less dangerous, but messy) splitting of the tank.
The valve might have opened because of overheating, but that likely would have released more water. More likely, there was a surge, or water hammer, that spilled a small amount.
Another likely cause of the puddle is deterioration of the rubber washers. The valve is subject to constant immersion in very hot water, so deterioration is faster than in a faucet washer. Although repairing the valve itself is trivial, it requires cooling the tank and partially draining the system, a nuisance -- so if it stopped leaking, just keep an ey on it fo further issues.
Finally, someone might have pulled the test toggle (the silvery handle at the top of the pipe -- good photo, BTW!) accidentally, or out of curiosity (and I've bumped it myself by accident, spilling a cup or so). As mentioned by others, it a good idea to test the valve every year or so, but sometimes it does not shut well afterwards, requiring a quick flip of the lever to reseat it... and sometimes it leaks, afterwards. Have a bucket underneath that overflow!