Wake Assist helps fix a stuck-on-wake bug suffered by some Mac users.
Wake Assist helps by providing a couple of automated clicks of the mouse on waking from sleep. These clicks help nudge a stuck Mac to fully wake up.
Wake Assist is a daemon process that runs quietly in the background. When the Mac wakes up Wake Assist checks for a user activity; if none is found, a couple of automatic mouse clicks are performed to display and hide the Apple menu.
This tool is aimed at users taking advantage of Apple's Energy Saver schedule to wake up their Mac without a user being present. This capability is often used to automate back ups.