Server time is simply the time to which the server's internal clock is set. This may or may not match the time in a given player's timezone.
Server time is important for day/night cycles, which impact such things as fishing, and the inhabitants of Pyrewood Village. It is also important for scheduling some events such as the Gurubashi Arena.
Note: Some newer servers may not have their server time set to match their stated timezone. The assumption is that Blizzard will fix this in due time.