Eye: The eye of the hook is where the tippet is tied. The eye can be up-turned, down-turned, or straight. In general, Spey style and salmon hooks have up-turned eyes, dry fly and wet fly hooks have down-turned eyes, and streamer, bass and saltwater hooks have straight eyes. The orientation of the hook eye is largely aesthetic and only comes into play when a knot used to attach the fly to the tippet is affixed to the shank and not the hook eye.
Shank: The shank is where the fly is tied and can be thought of as the backbone of the hook. The shank of the hook is usually straight, but can also be curved for Spey and Salmon style hooks, as well as living nymph hooks. The shank length is measured in hook eyes. If a hook is 1XL, that means the hook’s shank is one hook eye longer than the standard hook shank. In like, 1XS means the hook’s shank is one hook eye shorter than the standard size.
Bend: The bend is the most important part of the hook. This is the part of the hook that helps keep the fish attached to the hook after it has eaten the fly. There are many different types of bends. Some of the more common bends include: Model Perfect bend, Scud/Shrimp bend, and the Stinger bend. The bend style is based on the style of fly you want to tie. If you want to tie a streamer pattern, for instance, you would want to choose a stinger bend over a scud bend.
Point and Barb: The point is obviously the pointy part of the hook. Most modern hooks are chemically sharpened making them exceptionally sharp. For larger sized hooks, it is always good practice to sharpen the hooks with a file on a regular basis. The barb, traditionally used to keep bait on the hook, can also help keep the fish on the hook during the fight. One thing to remember about barbs is that many watersheds require barbless hooks. It is up to you to educate yourself on the rules where you fish.
Size: Hooks are generally sized in even numbers. The larger the number, the smaller the hook. That all changes once you get into large hook sizes. They are sized in “aught notation” starting at 1/0 (one-aught) and going up from there. There is no uniform standard for hook sizing. It is set by each manufacturer and can vary based on the hook style. As an example, a #2 dry fly hook and a #2 scud hook may not be remotely close to the same size.