The main feature, apart from the store etc. others mention, is that it is a game activation control system.
When you install a game disc that comes with a Steam key, or buy a game through steam, the record of the game ownership is added to your Steam account, permanently.
If you use more than one computer or buy a new machine, just copy the Steam directory to the other machine and install steam / log in with your account, and every game will be usable within a few minutes without any great reinstalls.
You can also just install steam on a new or empty machine and log in, and tell it to install your games on that machine. It takes a lot longer because all the game data has to be downloaded, but you will (eventually) have every game you bought that uses steam installed and working again.
No re-installing discs or having to put a game disc in to prove you own the game, everything "just works"..
That even works across different operating systems, if the game is available for the other OS - eg. if you have bought a game on a Windows machine then run steam on a mac or linux one, the game will be available if there is a mac or linux build, and vice versa if you bought while on mac or linux it's available to you on the other systems.
[The "Steam Machine" gaming system is linux based so a large percentage of games are available on linux systems].
With most games it also stores your save & progress, so you can switch to a different machine and carry on with the game rather than losing your progress and having to start from the beginning.
It also automatically installs game updates as they are released by the game makers, if you want it to & it can check or repair the game files if anything gets messed up on your computer.