This is a feature on some digital SLR cameras that allows the mirror inside the camera to be locked in the up position before taking a picture. The purpose of this is to help prevent the slight vibration normally caused by the mirror flipping up when the shutter button is pressed. It is normally used for shooting scenes with long shutter speeds when the camera is mounted on a tripod and using a remote control to release the shutter.
Under normal shooting conditions, locking the mirror in the up position is not necessary because the vibration from the mirror is so minute. Plus, you cannot see your subject in the viewfinder when using mirror lock-up.
NOTE: The a (alpha) Digital SLR cameras listed below use the two-second timer function as the mirror lock-up feature.