The PV term accounts for the work done due to either an expansion or a compression of volume (if constant pressure is assumed). If you have a gas and isolate it from the atmosphere so that it can't change its volume (i.e. so that it cannot do volume expansion work), and then heat the gas up, the change in H is equal to the change in internal energy or H=U. In this case, all the heat goes towards increasing the internal energy of the gas.
However, if the gas is allowed to expand against the atmosphere then only some of the heat will go to increase the internal energy of the gas, the other part of the heat will be lost to the surrounding atmosphere as the gas expands against the surrounding atmosphere (doing work on the atmosphere in the process). In this case the H will be larger than the U by itself and can be considered the sum of the two: H = U + PV.