Latent heat is the energy (see note below) released or absorbed during a phase change, where the temperature does not change. This is because all of the heat is used up in the phase change, rather than into changing temperature.
For a more in-depth explanation specifically of latent heat of fusion, see the link
For a more in-depth explanation specifically of latent heat of vaporization, see the link
Or watch the video shown below:
Latent heat is actually the total amount of enthalpy (a kind of energy) necessary to accomplish a phase change.
Phase changes are generally considered at constant pressure, rather than constant volume. Because a kg of say, 100°C steam, occupies a much greater volume than a kg of 100°C water, a lot of work has to be done to push the environment out of the way as that water expands to become steam. (The fact that vaporization does a lot of work is why we use steam to power a large number of the turbines in the world.)