Reluctantly means "with hesitation, doubt or dread." You might reluctantly walk into the dentist's office for your appointment, knowing that you will soon feel the pain of a root canal. Ouch!
The adverb reluctantly comes from the root word reluctant, meaning "unwilling, disinclined." When you do something reluctantly, you don't really want to do it. For example, if you answer a question reluctantly, you will first stall or try to change the subject. If your friend reluctantly agreed to help you move to your new house, you know she felt obligated to say "yes." Better buy her dinner, at the very least.