The Queen's Movement
The queen is, without a doubt, the most powerful piece on the chessboard. She can move as many squares as she desires and in any direction (barring any obstructions). In the diagram on the left, the blue dots indicate to which squares this particular queen may move. As you can see, she can cover 27 squares. This is a healthy percentage of the board, 42 percent. This is twice as much as the a rook. (However, performance will vary depending on the queen's position.)
She captures in the same way that she moves, replacing the unlucky opposing piece that get in her way. (She must, of course, stop in the square of the piece she has captured - unlike the knight the queen may not jump other pieces.)
The queen's power is so great that she is considered to be worth more than any combination of two other pieces (with the exception of two rooks). Thus it would be better, under normal circumstances, to sacrifice a rook and a bishop (for example) than to give up a queen.
Strategy Note: The queen's power also makes her too valuable to casually risk. Against skilled players, the loss of the queen is nearly equal to losing the game. For this reason, it is generally thought to be unwise to bring the queen out too early. The cluttered board makes her more vulnerable to entrapment.