Enthalpy is a “term of convenience” that is useful in the interpretation and application of Thermodynamics. Enthalpy is basically a measure of energy, but its main function is in the calculation and measurement of “flow energy” or gaseous energy (e.g. steam energy).
[Note (borrowed from mathpages.com): Enthalpy is not a specific form of energy. It is just a defined variable that often simplifies calculations in the solution of practical thermodynamic problems.]
The term enthalpy is defined as the sum of a system’s internal energy plus the product of its pressure and volume, or
H = U + P x V

where H is the enthalpy of the gas (in Joules),

U is its internal energy (in Joules),

P is its pressure in Pascals, and

V is its volume in cubic metres.
Put another way, Enthalpy = Internal Energy + Flow Energy.
Commonly a “system” may be a combination of solids, liquids and gases, in which case most of its internal energy applies to the solid and/or liquid components while the PV term defines the energy of the gaseous component. This is confirmed by looking at steam tables which show that the enthalpy of water (in its liquid phase) is almost identical to its internal energy.
Specific enthalpy (usually denoted by the lowercase letter ‘h’) is the enthalpy per unit of mass, often measured in units of kJ/kg.
Measurement or calculation of a change in enthalpy is usually more meaningful than the value itself. For instance, the energy inputs required to raise and superheat steam can be estimated from the change in enthalpy between each step of the process. The first table assumes that cold feedwater is injected into the boiler before being heated; the second table assumes that the feedwater is preheated to 100^{o}C before entering the boiler (in both cases taken to be at a pressure of 20 bar = 2000 kPa):
Enthalpy Rise without Feedwater Heating 

1 Start with cold water  Enthalpy of water at 25^{o}C  105 kJ/kg  Increase 
2 Raise water pressure to 20 bar  Enthalpy of water at 20 bar and 25^{o}C  107 kJ/kg  2 kJ/kg 
3 Raise water temperature to 212^{o}C  Enthalpy of water at 20 bar and 212^{o}C  909 kJ/kg  802 kJ/kg 
4 Evaporate at same temp & pressure  Enthalpy of steam at 20 bar and 212^{o}C  2798 kJ/kg  1890 kJ/kg 
5 Superheat steam to 400^{o}C  Enthalpy of steam at 20 bar and 400^{o}C  3248 kJ/kg  450 kJ/kg 
6 Total of enthalpy rises from point 1 to point 5 = 3248 – 105 =  3143 kJ/kg 
Enthalpy Rise with Feedwater Heating 

1 Start with cold water  Enthalpy of water at 25^{o}C and 1 bar  105 kJ/kg  Increase 
2 Raise water pressure to 20 bar  Enthalpy of water at 25^{o}C and 20 bar  107 kJ/kg  2 kJ/kg 
3 Raise water temperature to 100^{o}C  Enthalpy of water at 20 bar and 100^{o}C  418 kJ/kg  311 kJ/kg 
4 Raise pressure to 20 bar  Enthalpy of water at 20 bar and 212^{o}C  909 kJ/kg  491 kJ/kg 
5 Evaporate at same temp & pressure  Enthalpy of steam at 20 bar and 212^{o}C  2798 kJ/kg  1890 kJ/kg 
6 Superheat steam to 400^{o}C  Enthalpy of steam at 20 bar and 400^{o}C  3248 kJ/kg  450 kJ/kg 
7 Total of enthalpy rise from point 1 to point 6 = 3248 – 105 =  3143 kJ/kg 
It can be seen from step 2 of this second table that preheating of the feedwater to 100^{o}C reduces the energy required from the firebox by around 10%, hence offering a potential nominal fuel saving of this amount. [Note: if preheat is obtained from exhaust steam, then the resulting loss of energy from the exhaust will result in a small loss in exhaust system performance and thus a slight increase in cylinder backpressure and loss of cylinder efficiency. This loss, however, is far outweighed by the overall efficiency gain from feedwater heating.]
It can also be seen from both tables that the additional energy required to superheat the steam is small compared to the amount required to boil the water. The advantage of using superheated steam is that all of the energy in the steam can be put to use in the cylinder provided the degree of superheat is high enough to prevent the occurence (momentary or otherwise) of condensation in the cylinder.
For further information on the subject of enthalpy, see: