Internal gravity waves are like surface waves on the
ocean, they both propagate under the restoring force of gravity.
force is felt when there is a vertical variation in density such
as the density difference between water and air. When the density
difference is very large (at the interface between two fluids, like
water and air) waves are trapped at the interface and you have
surface waves. When the density varies gradually as in a
stratified fluid internal gravity
waves may exist. Such waves may move vertically upward
as well as horizontally.
In the atmosphere, the effect of internal gravity waves can be seen
on partly cloudy days. The rise and fall of the waves at just the
right altitude can make wave condense and evaporate, respectively,
and this leads to a banded cloud pattern.