Other forms: introspectively
Someone who is introspective spends considerable time examining his own thoughts and feelings. If you take to your diary after an unhappy break-up, you are being introspective.
The Latin word introspicere means to look inside, and that's what an introspective person does, metaphorically speaking. It's different from meditative and pensive in that they can refer to contemplating anything, whereas introspection involves specifically contemplating yourself.