The standard definition of uptime is how long your computer has been on since your last reboot. There are several ways to look it up, but the most commonly seen method (for IRC users, at least) is in channels, where one person displaying their uptime will cause anyone else who has a braggable uptime to do the same. In mIRC, the variable for your uptime is $uptime(system, 1)

Or, to put it simply, uptime is the geek version of "my dick is bigger than yours". Many IRC scripts will remember the largest uptime they have noted, so that even if you inevitably meet the Blue Screen of Death and your uptime gets reset to zero, you can still brag about how for a while, your penis was bigger than everyone else's.