Self-gravitation is the process by which the individual constituents of a large body are held together by the combined gravity of the object as a whole. Without it, stars, stellar clusters, galaxies, and groups and clusters of galaxies would all expand and dissipate. It also plays a role on even larger scales, being responsible for the deceleration of the the cosmic expansion until fairly recently in cosmological time (the Universe is currently accelerating in its expansion).
It is important to note that because gravity is much weaker than the other forces, only relatively massive objects become self-gravitating. Organic life, for example, are held together not by gravitation but by the chemical bonds between the atoms and molecules which make up our bodies.