The adjective amusing describes someone or something that makes you laugh. Something that you find amusing, like your favorite stand up comic, might be less amusing to your easily offended grandmother.
A pastime that's enjoyably diverting can also be described as amusing, like playing board games on a rainy day. Amusing comes from the verb amuse, which is itself from the Middle French word amuser. Interestingly, amuser meant "to stare at stupidly," and the English word originally meant "to deceive by distraction." The more benign funny and enjoyable meanings didn't arise until much later, but they eventually made the original meaning obsolete.