You can download the games as many as you want and will attache to your Steam account. So you can play it on any computer. However, you need a high-speed internet to download the online games.
You can use Steam's multi-player service after you download a game. You can choose the online users as opponents. It is very interesting, isn't it! You can also join a game groups and connect with others.
This platform is developed by Valve Corporation. This platform is available in 25 languages. Here is the website store.steampowered.com