Enthalpy, $H$ (kJ) is a measure of the total heat content of a system. It is defined as the system's internal energy $U$ (kJ) plus the product of the pressure $p$ (N/m$^2$) times volume $V$ ($m^3$):

$H = U + pV$

Because the $U + pV$ appears frequently in engineering calculations, the combination is given the name enthalpy. The enthalpy is the system's potential energy.

It's common to discuss the properties of fluids in terms of per unit mass:

$h = u + \frac{p}{\rho}$

where $h$ is the enthalpy (kJ/kg), u is the internal energy (kJ/kg) and p is the pressure (N/m$^2$) and $\rho$ is the density (kg/m$^3$).

For a fluid with a velocity, the stagnation enthalpy $h_0$ (kJ/kg) or total enthalpy, is the enthalpy a flow assuming the flow was brought to a zero velocity state isentropically (no heat transfer). It takes into account the kinetic energy of the fluid. It is defined as:

$h_0 = h + \frac{1}{2} v^2$

where $v$ (m/s) is the flow's velocity. The kinetic energy term does not have units of kJ/kg, however when kJ/kg and m$^2$/s$^2$ are multiplied by the control volume's mass, they both yield the required units of $kJ$.

[1] Fundamentals of Engineering Thermodynamics, Moran, M. J. and Shapiroa, H. N., John Wiley and Sons Inc, 2004.