In the experiment, a suspended parallel plate capacitor is held by a fine torsion fiber and is charged. An electromagnetic torque is measured due to magnetic forces since the capacitor is moving through the aether. The experiment determines if the passage of the Earth through the aether could be detected using electrical means.
Modern Trouton and Noble experiments have improved on the sensitivity of the original experiment by using higher voltages and better controlled experimental conditions. Some experimenters claim that even if the aether exists as originally proposed, Trouton and Noble wouldn't have been able to detect it using their apparatus. More recent experiments have not consistently produced a result in favour of the aether.
The Michelson-Morley experiment also provides a equivalent test of aether theories, but using optical rather than electrostatic means.
Trouton-Noble experiments are notoriously difficult to control. For example, a sufficient current flow in the test circuit will cause the device to act as a compass, aligning it with the Earth's magnetic field. For this reason, experiments which do not go to great lengths to rule out alternate explanations cannot be trusted: link 1 below is an example of this. Links 2 and 3 detail an experiment which, although it appears to be properly controlled, has not been repeated by an independent group.