Dictionary Definition: 

“A thermodynamic quantity equivalent to the total heat content of a system. It is equal to the internal energy of the system plus the product of pressure and volume.”

Selected from OxfordDictionaries.com

Functional Definition: 

First you must remember that in chemical reactions the breaking of bonds uses energy (endothermic) and the forming of bonds releases energy (exothermic). We typically measure energy as heat. Enthalpy (H) tells us how much energy in heat is released or used in a system and it relates back to the type of bonds we are breaking.  Some bonds are high energy such as the phosphate bonds in ATP that provide much if the needed energy in biological systems.

The equation for enthalpy shown bellow includes Gibbs free energy (G) summed with the absolute temperature (298 K) times the entropy of the system.