Most of us are familiar with waves. They are easily seen on the surface of the ocean or when you throw a rock in a pond. These are free-surface waves - waves that set up in between a liquid (in the examples mentioned, water) and a gas (air). Waves can also occur at the interface of two liquids with different density. If you put oil on top of water and disturb the interface, waves will propagate along the line in between the oil and water. If we now assume there are multiple interfaces (for example see the lines in the picture below where wind is blowing over topography), all on top of each other we would get waves that propagate along the interfaces which move the subsequent interface and so forth. If there are an infinite number of layers (continuous stratification), internal waves which propagate vertically and in both horizontal directions can be generated. Internal waves are found in the ocean and atmosphere as these are both naturally stratified fluids. The ocean has saltier, colder (more dense) water at its depths, and the atmosphere has a temperature gradient which sets up a density gradient.
What this looks like in the lab, after data is processed, is phases (crests and troughs) of waves propagating at angles from the vertical. The picture shown below illustrates a wave being generated by an internal wave generator created in our lab. The various colors represent the phases of the waves, but notice the colors are darkest near the generating mechanism. This is because this is the direction the energy is propagating and it decreases slightly further from the location of generation. This wave beam is shown in 2-D, and through time the phases would be propagating downward.