To reexamine something is to consider or inspect it again. A detective might need to go back and reexamine the scene of a crime several times during her investigation.
A scientist who's studying an unfamiliar bacteria will examine it, and then reexamine it again and again. And, if you still have an earache a week after starting antibiotics, your doctor may want to reexamine you. Whenever you take another careful look at something, you reexamine it. The verb reexamine adds the "again" prefix re- to examine, from the Latin examinare, "to test, try, consider, or ponder."