In the context of painting or fine art, a "study" is the term used for a practice piece, a quick painting done to capture the essence of a subject or scene, or a painting done to try out a composition, rather than a painting done as a final piece. A study is more refined or finished than a sketch and can include the entire composition (everything that will be in the final painting) or just small sections.
The reason for doing a study of a section is that you then focus on one particular part of a subject, and only this until you get it working to your satisfaction. Then (in theory), when you start painting on the bigger subject, you know what you're doing (with that bit anyway) and don't end up frustrated by one small part of a painting. It also avoids the problem of having a section of the painting overworked, which can look incongruous.