The descriptions others have given you – that it’s a FPS/puzzle game with a cool game mechanic – are good starts, but don’t tell you much about the plot/characters/style of the game, all of which are so integral to what’s made it so popular. If you want a little more detail (without any real spoilers), here goes.
You (playing a young woman named Chell) wake up in a laboratory where you must complete 19 levels of increasing difficulty, equipped only with a remarkable device that shoots portals. You don’t even get the portal gun to start with; first you’re trained in the very basic mechanics of going in one portal and out the other. Step by step you gain access to the gun, at which point the tests get more and more difficult. Puzzles involve jumping, manipulating your environment, working with physics/momentum, and above all, figuring out where to place your portals.
The game would be lots of fun if it were just these puzzles, but there’s also a bigger plot picture involved. What are the tests for? What is the real aim here? What happens when the tests are over? And where the heck is everyone?
The atmosphere of this clean, glossy white laboratory environment is increasingly creepy, especially when you discover you’re utterly alone, except for the disembodied robotic voice of GlaDOS, an AI who explains, encourages, manipulates, cajoles and taunts you depending on the circumstances. ‘She’ isn’t exactly what she seems, and neither are the tests, the inatimate objects, or the laboratory, as you’ll learn.
There’s a lot of humor in Portal, most but definitely not all coming from GlaDOS herself – who’s sort of like 2001’s HAL if designed by the Sirius Cybernetic Corporation of the Hitchhikers books. The game is fresh, funny, warped, clever, and over all too soon … but wow, what an ending! Justifiably famous. Plus there are cool extra/advanced levels/achievements once you’ve played all the way through.
And yep, you can buy it separately, at least through Steam.
BTW, Portal was recently named “Game of the Year” at the Game Developers Choice Awards, something of an upset for a three-hour puzzler when considering its competition was a huge critical/audience hit like Bioshock.