Exobiology is the study of the origin, evolution and distribution of life within the context of cosmic evolution [as stolen from the title of a review paper: G. Horneck, Planet Space Sci. 43, 189 (1995)]. The term was first coined by Lederberg in 1960. Basically, it's the science of trying to figure out how and where life first developed, and how it may have been distributed throughout the universe. As one might guess, it's a very broad field, involving astronomy, planetary sciences, organic chemistry, paleontology, and much of biology.