If you're gleeful, you're delighted or joyful. The sound of children's gleeful laughter is one sign of a successful birthday party.
When you feel gleeful, you're more than happy: you're exuberant and joyous. A friend's gleeful face tells you she's gotten great news or heard a hilarious joke, and gleeful kids will sometimes even scream with joy. In the 17th century, the alternate adjective gleesome competed with gleeful — both come from an Old English root, gliu, which means "mirth, play, sport," and also "music" and "mockery."