A higher frame rate is better. However, when you're actually playing a game, the display's refresh rate does effectively limit the frame rate – if you have an 80hz display and your computer is capable of outputting 120 FPS, your screen will still only be able to show 80 different images per second.
60hz monitor is only capable of outputting 60fps
Explanation:
144hz refers to the display's refresh rate - aka how many times it can draw a new image within the space is a second. Framerate refers to the number of complete images that your computer can generate within a second. For the best results you want the two to match, or at the very least for one to be a multiple of the other. Because when they're not, you get this:
