In the BOSU manual, the first section deals with balance exercises. Most of these involve standing on the BOSU and then doing additional things to make this more difficult, such as head movements, arm movements, or closing the eyes.

While the manual has a number of decent exercises in it, it doesn't go into all the possible variations for space reasons. What I didn't bank on was that some of these variants lent themselves to better, more memorable colloquial names than one would expect.

The most basic involve raising and lowering both arms, straight up and down, in front of the body:

Two-armed headcrab zombie slash
Raise and lower both arms together.
Godzilla
Raise and lower both arms antisynchronously—when one is raised, the other should be lowered.

Others involve rotating the arms in front of the body:

Floral Arrangement Fluffer
rotate the left arm counterclockwise and the right arm clockwise. Do this synchronously—when one arm is on the inside loop, the other should be, too.
Danger, Will Robinson!
Rotate the left arm clockwise, right arm counterclockwise. When one arm is at the top of its loop, the other should be on the bottom.

That said, nowadays I spend most of my stand-on-a-BOSU time watching TV shows and am less inclined to make large arm movements except during the boring parts.