Commonly used in compound nouns like アミューズメントパーク (amusement park) or アミューズメント施設 (amusement facility). As a standalone noun, it refers to entertainment or fun activities.
We went to an amusement park as a family on the weekend.
This facility has a variety of amusements.
At this hotel, you can enjoy a variety of amusements.
He has worked in the amusement industry for a long time.