A bridge is a certain type of electrical circuit with resistors placed in a way which allows an observer to figure out the resistance of an unknown resistor, if the resistance of all the others are known. A path from a source diverges into two resistors, which form a square shaped network with two other resistors. The sides of the square are then connected in the middle by a fifth resistor, running down one of the square's diagonals. Here's a diagram of a typical bridge setup:

                             R1
    |-------------------|     |
    |                   |     V 
    |                   |     
    |                   ---/\/\/\--
    |                   |        /|
    |                   \      \  /
    |            R2 --> /    /    \  < -- R3
    |                   \  \      /
   /+\                  |/        |
  /   \                 ---/\/\/--|
 |  V  |                          |
  \   /                      ^    |
   \-/                       |    |  
    |                        R4   |
    |                             |
    -------------------------------

R5 is that terrible looking thing crossing the middle of the bridge. It's supposed to be a resistor going across the two nodes, one formed by the intersection of R2 and R4, and the other formed by the intersection of R1 and R3. Anyway, bridges have special properties. If (R2)(R3)=(R1)(R4), the current passing through the fifth resistor will be zero. This will help when we want to figure out the resistance of the unknown resistor.

Because the voltage across the middle is zero when (R2)(R3)=(R1)(R4), we can replace R5 with a voltmeter, and know that this condition is true when the voltmeter reads zero. If you wanted to find one resistor's value, you could then replace another resistor with a decade box that has known resistances and adjust until the voltmeter that crosses the bridge returns zero. When it does, the equation (R2)(R3)=(R1)(R4) is satisfied and you can solve for the desired value.