BMS, short for Be-Music Source is a rhythm game which simulates several BEMANI rhythm games using a file format originally designed by Urao Yane: ".bms". BMS initially simulated Beatmania, but it later simulated its successor, Beatmania IIDX, as well as Pop'n Music, and KEYBOARDMANIA.
The defining aspect of BMS as a file format is that it enables the usage of keysounds, which are small audio files that are attached to a falling note within the game. Keysounds can technically be anything, as they are just audio files, but are usually used to convert the notes of a song to be playable within the game.
The defining aspect of BMS as a game is that the vast majority of BMS works are original songs, illustrations, charts, and videos made by anyone who decided they wanted to make BMS. Rather than using BMS as a way to directly emulate and experience Beatmania, people used BMS to create their own original content to share with others.