Frames per second (fps) is exactly what it sounds like - the number associated with the term is telling you how many frames your game is running at every single second. For example, if a game says it runs at 30fps that means that every second there are 30 frames shown.
Without going into the extreme details of explaining how our eyes/camera shutters process individual frames in a moving image - to give reference, most movies run at 24fps. In video games, you typically want at least 30fps and the more the better. The lower the fps, the slower/laggier the game runs (for example, if your game runs at -10fps you probably are watching a slide-show rather than playing a game). The higher the number, the faster/smoother the game will appear visually.
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