The adjective amused means "pleasantly occupied" or "entertained," like when you amused yourself by inventing funny stories about the people in the mall and what they had in their shopping bags.
Amuse comes from the Middle French word amuser, meaning "to divert the attention, beguile, delude." If on a boring rainy afternoon, you amused everyone, you entertained everyone, probably making them laugh. If you were ever told, "I'm not amused," however, this goes beyond not finding something funny — that person might be angry and offended at something you said or did.
