Someone who considers other people's feelings has the quality of thoughtfulness. It takes real thoughtfulness to comfort a friend who's recently lost his pet cat.
When you remember to bring doughnuts for everyone at work, that's thoughtfulness, and it's thoughtfulness that inspires you to send your grandmother a thank you note for your birthday gift. Another kind of thoughtfulness describes deliberate thinking before doing something. It might, for example, require some thoughtfulness to figure out how to hook up your new TV. The word comes from the adjective thoughtful, which originally meant "moody or anxious," but came to mean "considerate" in the 1850's.