In chemistry "delta H" is the change in enthalpy of a system. Change in enthalpy is measured as the sum of the change in internal energy of a system plus the change in the product of the pressure and volume of the system.
At a constant pressure the change in enthalpy equals the heat given off or taken in by the system. If the volume is constant, the heat released or absorbed by the system equals the change in internal energy of the system. In reactions with solids and liquids, there is only a small change in the volume of the system, so the changes in enthalpy and internal energy are very similar. In reactions that involve gases, they can be very different.