Input lag is a measurement of the delay between the time you enter a command on your keyboard, mouse, or controller, and the time it registers on your screen. A low input lag is crucial in "twitch" (time-sensitive) video games where fractions of a second matter.
Input lag is different from response time; the latter is an indicator of how fast a pixel can go from black to white and back again on a particular monitor. Monitor manufacturers tell you about their "gray-to-gray" (GTG) response times, which tend to be lower. Although response time isn't as important as input lag, response times in excess of 5ms can sometimes produce images that feel blurry or have ghosting, which can affect your gameplay. So if you have the option of lower response time, other things being equal, you'll want to take it.