Astrophysics is concerned with the physical processes associated with the celestial bodies and the intervening regions of space. It deals principally with the energy of stellar systems and the relation between this energy and the evolution of the system. Astrophysics can be broken down into observational (uses the electromagnetic spectrum) and theoretical (uses analytical tools) astrophysics. (There is no such thing as experimental astrophysics because the scales and objects being observed are far too large or far away to experiment on with modern technology.)
Some schools use the term astronomy to describe essentially the same thing, although most agree that astronomy describes the qualitative version of astrophysics. Astrophysics and physics are often combined into one department.
Astrophysics is a subdiscipline of physics, and is also considered a branch of astronomy. It is also related to planetary science.