Steam is a computer program made by Valve, developed for the release of their first game using the Source engine, Half-Life 2.
The objective of Steam was, originally, to download and install patches for games automatically, in the least intrusive way as possible. However, it has evolved quite a bit since then, and now it's much more than that.
Steam has a very safe, online store, where you can purchase a huge variety of games, growing every day, from all developers and of all genres, from first person shooters to casual games. Every game you buy is then associated to your account, meaning that you can download and install Steam in any computer, log in your account and redownload all the games you've got for free, without any kind of limit.
Steam also has a large library of free media, ranging from free game demos to trailers and other videos (such as the Meet the Team machinimas Valve created to advertise one of their games, Team Fortress 2).
Every weekend, Valve makes "weekend deals", which are special discounts for one or more games, which can be huge (75% off). Sometimes, there are no weekend deals, and sometimes too, there's a 100% discount. Those weekends are called "free weekends", and for 3 days (friday, saturday and sunday) you're free to download and play a certain game with absolutely no cost, and you're given the option to buy the game after the offer has ended.
Since August of 2007, Steam received a big update called the Steam Community, which added features akin to popular social networks, but oriented to gaming. For instance, chatting in-game and organizing events for groups of people.
As a computer program, Steam has excellent performance, and although it freezes every now and then, you shouldn't have any problems with it. You can also customize the program with skins, that change the colour scheme and whatnot, ideal to make Steam fit with your computer if you've installed custom themes, or if you just don't like the default looks.
With the arrival of the Steam Community, Steam got the added functionality of working with pretty much every single game out there, letting you add the games to your Steam collection as shortcuts and then play them with some added functionality (such as the overlay that lets you chat in-game).
Overall, Steam is a very practical, user-friendly, but powerful, online gaming platform. Highly recommended.