Recall that a Wheatstone bridge involves a variable resistor in one leg, and an unknown resistance in another leg. An excitation voltage is applied to two opposite corners of the bridge, and voltage is measured across the two orthogonal, opposite corners. The variable resistor is adjusted to produce a null in the measured voltage. In a noise bridge, the variable resistance is replaced by a variable resistance and variable reactance in series. The excitation signal used is broadband noise, and the null measurement is performed by a receiver.
Most hams never bother with a noise bridge.
Every so often, though, a ham will put up an antenna which ought to work but doesn't, or doesn't work at the proper frequency, and a noise bridge provides information on why it doesn't work and how to fix it. Most importantly, it does so without causing the inadvertent transmission of signals on prohibited frequencies. The ARRL's Handbook or their Antenna Handbook discuss construction of noise bridges. Since the noise generator would typically make a relatively high level of noise that would be attenuated down by precicesly calibrated attenuators, one can know how much noise was required to equal the intrinsic noise of the receiver, and thus infer its performance. In this case the noise source is used to inject at the input of a potentially complex system some signal either through a directional coupler or by switching the input.