Official documentation released by a game's developers listing the changes in an update: bug fixes, balance adjustments, new or removed content, performance work, and changes to systems and mechanics. Patch notes are the main way developers tell players what changed, and for competitive games they matter a lot, because a balance change can shift which strategies are viable. League of Legends is the classic example: in 2014 Riot standardised its patch cadence to roughly every two or three weeks, and each patch changes the effectiveness of strategies in the game, so keeping pace with the changes became part of playing it. For Early Access and indie games, patch notes are also the closest thing to ground truth for how a system currently works, which is why guides on this site check claims against the developer's own notes rather than secondhand summaries. Many developers now pair the notes with dev blogs, videos or preview streams that explain the reasoning behind a change, which helps players predict where the game is heading.
For new players
Patch notes tell you exactly what changed in an update. In competitive games, read them before you play, since balance changes can move which characters or strategies are strong.