Your tamagotchi has died. On various versions this can look like an alien in a UFO, an angel in the stars, or a gravestone. Press A+C to get a new egg. See here for more on Tamagotchi Death.
Your battery has died! On various versions it looks like a crossed out battery, a tiny crossed out battery, or a tamagotchi battery alerting you that it is low on power. Change your battery! See here for more on which kind of battery your tamagotchi takes.