Definition 1: The amount of heat that will flow through a square foot of a building cross-section experiencing a temperature difference of 1 degree F.
Definition 2: The total thermal conductance of a building assembly (wall, floor, ceiling, etc.), including the indoor and outdoor air-film resistance of the assembly. The U-value when multiplied by the effective temperature difference between the indoors and outdoors, including the effects of solar and sky radiation (the "sol-air" temperature) where appropriate, will yield the normalized (per unit area) heat flow across that building composite. The units of U-value are Btu/hr-ft2-oF.