Compact binoculars are generally defined as those with lenses of 32mm and less. They’re small and light, and specifically designed for carrying for long periods without getting too heavy. They also fit in your hand comfortably.
The smaller varieties, such as 25mm aperture will even fit in a pocket. This means that they can be used as opera glasses, or at sports grounds during the day.
Because the aperture isn’t large, compact binoculars aren’t the best for astronomy. While they’ll show you the Moon and bright stars and planets, they don’t let in enough light to show you the darker things in the night sky.