From AMS Glossary
The hydrograph, for a given river basin, that would theoretically result from a continuous, constant excess rainfall rate per specified period T resulting in a runoff volume of 1.00 unit depth (e.g., 1.00 cm or 1.00 in.) over the basin for each period T.
The curve has a characteristic S-shaped rising limb, reaching a constant final discharge rate equivalent to the constant excess rainfall rate multiplied by the area of the basin. An S-curve is constructed from a series of unit hydrographs of period T by the simple process of successive displacement by T and summing up the ordinates (discharge values). In theory, the unit hydrographs for storms of any duration may be derived from the resulting S-curve.