The Alarm Egg resembles a cross between a spotted egg, a spotlight, and a ringing alarm clock, most likely playing a pun on an egg timer.
The main objective of the Alarm Egg is to "wake up" Claris or Elliot in NiGHTS into Dreams so they can not help NiGHTS. In the beginning of each level, the Alarm Egg will appear and start winding itself if Claris or Elliot do not proceed to merge with NiGHTS. Also, when your timer at the top of the screen hits 0, the current dreamer will fall out of NiGHTS and hit the ground below, causing the Alarm Egg to appear and wind itself.
Once the Alarm Egg materializes and finished winding, it'll chase after the dreamer. Should the Alarm Egg's light spot the dreamer, it'll cause the dreamer to fall backwards into the air. If Claris or Elliot fail to get up in time to avoid the spot light of the Alarm Egg, they'll wake up and the player will receive a Night Over.