Frames Per Second refers to the rate of images that can be generated per second and displayed to your monitor. Instead of displaying a constant image, computer displays need to illustrate motion as a set of images.
A lot of information needs to be processed for a Graphics Card to generate an image. This involves a heavy amount of shader compilation, lighting calculations, shadow calculation, textures, image sharpening, rendering settings, and many other unlisted processes.
On average, at 60 FPS, it would take a GPU roughly 16 ms to display each frame to swap to the next image. The higher the framerate, the less time that image is displayed.
Aside from being the entire reason a computer can display useful information, higher FPS values result in better response time, according to multiple studies. If you'd like to see a comprehensive review on how FPS improves competitive eSports scores, check out these videos by Linus Tech Tips.
As studied and experimented, a higher FPS results in better gamer-response time in competitive shooters, due to the lower frame time and lower input delay. Since a higher framerate results in lower time between frames, there's a quicker response time for your mouse or keyboard inputs in game.
This is a great question! There's many factors as discussed before that contribute to frame generation. Typically, the quick and easy solution is to lower your graphics settings, which will reduce rendering strain. If you're using an NVIDIA 20-Series GPU or higher, some games give you access to DLSS™. Deep Learning Super Sampling (DLSS™) is a technology for NVIDIA GPUs which uses "deep learning" to make a sharpened image of the original lower resolution image. Essentially, it renders your game at a lower resolution, and upscales it to a higher fidelity, improving performance.
Similarly, if you have an AMD Ryzen™ GPU, some games will feature AMD FidelityFX Super Resolution, or FSR. These technologies are very similar but do perform differently. They both improve framerates by the same means. Do not see one as greater than the other, as they are both technologies that cannot easily be compared due to the intensive differences in graphical architecture. FSR and DLSS are both wonderful technologies that improve performance for gaming.
If you're experiencing sluggish or non-ideal FPS, always ensure your graphics drivers are up to date.
As pictured, this is a chart showing the size difference in pixels between resolutions. You may assume that 1080p is almost double the resolution of 480p, but actually it's quite more than that! And 4K (2160p) is actually more than just 1080p doubled. Why does this matter? The higher resolution you use, the harder and more strain you put on your GPU. The more fidelity that needs to be displayed, the more detail shown. 1080p is a gold-standard for modern gaming, with more recent pushes to 2K (1440p) and sometimes 4K (2160p).
The Refresh Rate of a monitor is just an extension of framerate. To put it simply, the refresh rate is how many frames your monitor can display per second. If you have a 60 Hz monitor, you will be able to show 60 FPS. 144 Hz will show 144 FPS, and so on. If you plan to do more serious competitive gaming, it's recommended to go for a 144 Hz monitor or higher.
Casual games are wonderful to play if you're more of a kick-back gamer. A high framerate in your casual games will give you a smoother experience, especially if you cap your FPS. Capping your FPS refers to when you lock your maximum FPS in a game to a value like 60 FPS. This means you will only use the power you need to reach that capacity, without using all your power available to make more than the needed rate. You won't benefit much from trying to play your cute farming simulators at 144 FPS.