enthalpy
Imagine inflating a balloon in the open air. To grow, the gas inside must not only store its own internal energy but also shove the surrounding atmosphere out of the way, doing work p V just to make room. Enthalpy is the bookkeeping quantity that bundles both together: the energy actually inside the system plus the push-work needed to carve out its space at the ambient pressure. It answers the question 'how much heat must I supply if I let the system expand freely at constant pressure?'
Formally the enthalpy is defined as H = U + p V, where U is the internal energy, p the pressure and V the volume. Its natural variables are entropy S and pressure p, and its differential is dH = T dS + V dp (plus mu dN for open systems). This makes it the Legendre transform of the internal energy that trades the volume V for its conjugate variable, the pressure p. For a process at constant pressure with only p V work, dH equals the heat exchanged, so the heat capacity at constant pressure is C_p = (dH/dT)_p.
You meet enthalpy everywhere heat is measured at constant (atmospheric) pressure: chemical reaction heats (exothermic means delta H < 0), phase-change latent heats, and steady-flow devices like turbines, throttles and heat exchangers, where the Joule-Thomson expansion conserves enthalpy. A common trap is to call H a 'heat content' in general — heat is not a state function, and dH equals heat only under the constant-pressure, no-other-work proviso.
Heat one mole of an ideal gas at constant atmospheric pressure. The heat needed to raise its temperature by delta T is Q = C_p delta T = delta H, and part of that heat, p delta V = R delta T, leaves again as work done pushing back the atmosphere; the rest, C_v delta T, stays as internal energy. Hence C_p = C_v + R for an ideal gas.
At constant pressure the supplied heat equals the enthalpy change, not the internal-energy change.
Enthalpy is a state function of the system alone; the p V term is built from the system's own pressure and volume, so H is well defined even for processes that are not at constant pressure — it is only its interpretation as exchanged heat that needs constant p.