It's not clear where crispy, crunchy, and nutty, coconut shrimp entered the snack-food lexicon—they might be Caribbean, possibly Polynesian, or most likely, a purely American tiki-bar invention—but they're popular enough that you'll find 'em everywhere from Thai restaurants to Irish pubs.
Conceptually, they're simple: replace the crumbs in a standard breading with dried, shredded coconut, and deep fry. When done perfectly, you end up with a significantly crunchy, thick crust of aromatic coconut surrounding a center of juicy, perfectly cooked shrimp without a hint of rubberiness.
You can use whatever dipping sauce you like, but my favorite is a sweet chili sauce loosely based on a Thai nam prik pao, made with dried chilis, palm or brown sugar, vinegar, garlic, and fish sauce.
There are just a couple of keys to keeping your shrimp perfectly juicy and crisp. First, use large shrimp that are at least 12/15 count to a pound. In most places, these shrimp will be labeled "jumbo," though shrimp size labels are not regulated, so always make sure to check the count-per-pound instead of the sizing. If your shrimp are too small, the ratio of breading to shrimp will be off, and they'll cook through too quickly, turning rubbery as the crust crisps up.
The standard breading procedure of flour, followed by egg, followed by coconut works here, but I like to mix a bit of panko-style bread crumbs in with my coconut to give the shrimp an extra-crisp crust. Adding a couple of tablespoons of flour to the egg step also creates a slightly thicker, crisper coating.
Finally, make sure to clean off the tails before you take'em for a plunge in the fryer, which'll give you a convenient handle to pick'em up by when you're knocking them back.