Installation means to put a program on a computer so that the computer can run it.
Most programs are stored in special ways to make them smaller, or to gather all the different pieces of a program up into one big piece. Before it can be used, though, the program needs to have these changes undone. Some programs also need to know extra information about the computer it is going to run on, so while it is installing, it will figure out what it needs to know and write it down for later.