2. To divert or to please with anything light or cheerful.
3. To amuse someone with an anecdote, by telling him or her a story; to amuse oneself with a puzzle, with, by, or in sketching; to be amused with a toy or whimsical person, by telling a story about an incident.
4. To cause (time) to pass pleasantly, to entertain agreeably; to "beguile", to while away the time, to enliven.
5. Etymology: from Middle French (1400-1600) amuser, "divert, cause to muse;" from à, "at, to" + muser, "ponder, stare fixedly".
The current meaning "divert, entertain" did not emerge into usage until the 17th century, and the most common application of the verb in the 17th and 18th centuries was to "deceive, cheat". Such meanings seem to have developed from an earlier "bewilder, puzzle", and pointed back to an original sense of "make someone stare open-mouthed". This is thought to link with the probable source of muser, namely muse, an "animal's mouth", from medieval Latin musum from which the English word muzzle came.
Everyone should keep in mind that there is no connection with this muse and the mythological muse from which music and museum are derived.
The sense of "divert from serious business, tickle the fancy of" is recorded from 1631, but through the 18th century, the primary meaning was "deceive, cheat" by first occupying the attention of a person, or people.