Go read about terminal server. There are many out there free and paid. Depending on what you are actually doing they have different features.

I suspect you will not be happy playing games via a terminal server. The key to most games is the video. Now you must send the video over the network. When you consider how much data is transferred between the video card and the monitor it tends to be impossible to get those rates remotely. There are some terminal server that pretend they are a video card but if that worked so well nobody would buy expensive hardware when your could have a software video card.

Certain types of application lend themselves to remote operation. Software that is licensed to a machine is one example. You do not want to buy a second copy so you run it remotely. Another is database. You want your disk access as fast as possible and don't want to run that over a network.

This is basically going back to the mainframe days where you have a large central machines and dumb terminals attached to them. You pretty much have the same limitations that moved the computing to the desktop.