A frame is an image, which means the frame rate is the number of images being rendered in a second.
In the context of game development, the game engine runs in a loop so the frame rate is how many loops have been completed by the game engine (this loop includes reading user inputs, processing AI logic, processing other systems such as AI, Physics or Audio, and finally rendering).
The most common frame rate in games is 60 Frames per Second (or FPS), which means the engine has 1/60 = 0,166667 seconds (or around 16 milliseconds) to process all systems and render the game state to the player’s screen. Games running on low-resource platforms (such as mobile) or needing high complexity systems may run at 30FPS, while games focused on high-fidelity visuals can push up to 120FPS and above: 60FPS is the common target, but the developer can make its own choice regarding this target framerate.
To note: Frame Rate is also limited by the capabilities of the target monitor for rendering and is usually locked by it to prevent screen tearing (see VSync)