Sea waves break as their bases are slowed down upon reaching shallow water and their crests surge ahead. Cloud waves break in the same way. The difference in air currents, or shear, will cause the tops of the clouds to crest over the base giving it that "wave" appearance.

Let me explain why this happens in a bit more detail. From top to bottom, our atmosphere has layers. Kelvin-Helmholtz clouds occur when there is a temperature inversion with a warm, light (less dense) layer of air at the top of the cloud and a cool, heavier (more dense) layer at the bottom. When the upper layer of air is moving at a higher speed than the lower layer air, it may shove the top of an existing cloud. 

This causes the clouds to look like breaking waves in the ocean, because it is the same physical process. Clouds that look like waves are rare and beautiful so please snap a picture and share if you ever see them! Fun fact: These clouds are named after Hermann von Helmholtz and William Thomson, Lord Kelvin, physicists who studied turbulent airflow.