This is a device that can be used to find the resistance of a 4th resistor, given the resistance of 3 other resistors. It works by the same principle as the potential divider.
It can be thought of as two potential dividers with the same $\frac{V_1}{V}$ ratio. This ratio is only the same when the galvanometer shows a zero deflection. Consider the diagram:
The metre bridge
This is a practical implementation of the Wheatstone bridge. The resistances of the sections $R$ and $S$ can be varied by sliding the connection at $Y$ until the galvanometer reads zero.
By assuming that the resistance is uniform with length of wire, the ratio of the resistances $P$ and $Q$ can be found: $$ \begin{equation}\begin{aligned} \frac{R_{P}}{R_Q}&=\frac{R_R}{R_S}\\ \therefore \frac{R_{P}}{R_Q}&=\frac{d_R}{d_S}\\ \end{aligned}\end{equation} $$