MTT assay is a color based cell viability assay(cell proliferation assay). ie To determine the cell growth and the action of a drug, cytotoxic agent on the cell etc.
principle is that, cell utilizes the yellow tetrazolium salt which is metabolized by mitochondrial succinic dehydrogenase activity of proliferating cells to yield a purple formazan product by the mitochondria of viable cell . formazan is nothing but a dye (artificial chromogenic product) helps in reduction of tetrazolium salts by dehydrogenases and reductases.
In vivo, the dehydrogenase uses NADH as a cofactor and an many use active site histidine residues in the imidazolium state.
Intramolecular pi rearrangement within the nicotinamide ring eliminates a hydride ion which is nucleophilic towards carbonyl groups and other electron deficient atoms on the substrate (cofactor is now in the NAD+ state). The imidazolium nitrogen on the histidine is deprotonated by the substrate.
The tetrazolium compound is reduced in much the same way to obtain the formazan from the nucleophilic hydride by the cofactor. As mentioned in the other comment it is this reduced product that is measured and allows measurement of dehydrogenase activity.