In Handbook of Hatches by Dave Hughes, pages 87/88: “Learning to add wiggle to your emerger and dry-fly presentations will do more to increase your catch than any other single thing you can do, when you’re fishing over rising trout. Wiggle is important in the cross-stream reach cast. It is critical in the downstream wiggle cast. It can even help you take a few more trout in up-and-across-stream presentations. A little wiggle added to almost any cast will increase the likelihood that your fly will get a free drift. That will always catch you more trout, whether you’re fishing a mayfly emerger, dun, spinner, or any other insect imitation on the surface.“

A nice fish to a chrionomid (midge) emerger.

Here is a short video that demonstrates the words describing the wiggle cast at Sexy Loops (remember shooting a bit of line makes all the difference on imparting the wiggles).