Blokus is an abstract strategy game in the same general family of games as Hex or Twixt, but with more strategic depth than either of those games.
Each of four players has a set of 21 pieces that are all possible polyominoes containing one to five squares. (The Tetris shapes are the five possible polyominoes with four squares; Blokus shapes run from 1 square to 5 squares in size, one of each possible configuration.)
It is played on a square grid. Your objective is to place all your polyominoes on the board while blocking others from doing so. Your first piece placed must cover your corner square. Each additional piece placed must but diagonally adjacent to another of your pieces, but may not share a square side with one. It may, however, share square sides with other players' pieces, so color networks often interpenetrate each other.
Unlike Hex and Twixt, blocking an opponent does not mean building a line they cannot cross; indeed, given the placement rules, this is hard to do. Instead, it means seizing territory such that the places in which other players can play are constrained. It's all about the corners -- maximizing the number of corners, and space around them, where you can play, while minimizing space available to others.
Blokus is an excellent strategy game of its type -- that is to say, too colorless and purely cerebral for my taste, but admirably tight and with considerable strategic depth. And the colors and patterns created during play are appealing as well. There is one element of the marketing that deserves note, however; the box says it's for "ages 3 and up," which is, when you get down to it, absurd. While the rules are simple enough that a 3-year old can certainly play it, the strategy is complex enough that you'd need to be a middle schooler or such to have a hope of playing it well.