Celestial mechanics is the application of mechanics to celestial objects, e.g., planets, galaxies, moons, etc. Mechanics, in turn is the branch of physics dealing with forces and motion. More specifically, dynamics is the study of forces and resulting motions, e.g., orbits, and statics is the study of forces in the absence of motion, e.g., why the inside of the Moon doesn't collapse to allow it to grow smaller, and kinematics is the study of motion without regard to the forces that cause it.
For example, Kepler's laws, which describe orbits (Keplerian orbit) fall under the heading of kinematics, whereas Newton's laws, which describe how forces bring about orbits, fall under dynamics. Celestial mechanics as "mechanics focused on astronomical phenomena", includes some focus on the dynamics of orbiting bodies, and has developed techniques of determining long-term (secular) changes, i.e., perturbation theory.