Belonging is a sense of fitting in or feeling like you are an important member of a group. A really close family gives each of its members a strong sense of belonging.
When you belong, you are an official part of a group ("She belongs to the French club") or you're compatible with certain people or suited to a specific place ("I just belong in nature"). A feeling of belonging describes this sense of truly fitting or meshing, especially with friends, family members, or other sympathetic folks.