Basically, the game works like this. You have two players, one who uses black pieces and the other who uses white pieces. The amount of pieces that each player gets is, in theory, limitless. In addition, you have a Go board, which is usually 19 x 19 and composed of squares. The player who has black pieces goes first, and puts one piece (or, as Go fanatics might call them, stones) on any intersection between two lines. This includes the 4 corners of the board and all along the outer edges. White goes next, and places their piece on the board. Then, it alternates back to black, then white, etc. You have only two options for a turn: put a stone on the board, or pass.
Now, how does one win the game? Typically, games end by 2 methods: one player resigns, or the game goes down to the wire and players have nowhere else to put their stones (or, the spots where they could put their stones down would do nothing to change the game situation). To calculate the score at the end of the game, you need to count how many "intersections" you control. This is called your territory Your territory obviously includes the intersections that have your stones on them, but also can include empty intersections which are surrounded by your stones, excluding diagonals.
The fun part of this game comes with the capturing. If you have your own pieces surrounding another piece (or pieces -- it's certainly possible to capture fifty or more of your opponent's pieces in a single turn), you capture it and your opponent's stone is removed from the board.
There's a lot more to the game of Go than what I posted up here. You might want to check out the wikipedia entry for Go for additional information.
It's probably a case of those stones being trapped in within a range of opponent's stones in a way that there is no way "out." Thus, instead of wasting time playing stones, the players probably take those "dead" stones out since they both know those stones will be inevitably captured.