A mountain wave is caused by the vertical displacement of air flowing over the mountain. Think of a large submerged rock in a fast flowing stream. Mountain waves occur when the jet stream is strong and the atmospheric temperature profile is just right, which can happen in the winter. Mountain waves are stationary or very slow moving (because their cause, the mountain, isn't moving) unlike the traveling waves at the beach which move toward shore. Even though the mountain wave isn't moving, the air is flowing through the wave rapidly. Sometimes the wave is accompanied by turbulence.

"Lose control" means exactly that. The mountain waves can have strong updrafts and downdrafts which toss the plane around no matter what the pilot does. Eventually the plane will come out of the wave and the pilot can regain control.

As in your example, pilots will try to avoid the areas and altitudes with strong waves.

Finally, I'll add my thanks for Putt4eagle's story, too.