A period of inactivity, with no moving or growing, is dormancy. A bear is in a stage of dormancy when it hibernates: both its heart rate and body temperature become very low and it doesn't do much besides sleep.
You can describe any state of deep sleep or profound calm and quiet as dormancy, like your weekend of dormancy after an incredibly hectic week at school. It's mainly used in a more scientific way, though, to talk about the dormancy some animals go through in the winter in order to save valuable energy or the dormancy of certain plants during a dry season. Other things that are temporarily inactive, like volcanoes, also experience dormancy.