The most obvious part of a hook is its point. The point is what sticks in the fish - or you if you aren't careful. Hook points can vary a lot, too. Most are triangle shapped, with a flat outside edge and cutting edges at angles to it toward the inside of the hook. Points can also be round or diamond shaped but the most important thing is to have a sharp hook. The triangle shape hook is easiest to sharpen with a file or stone.
The eye of the hook is at the other end from the point. It is where your line attaches to the hook and can be very small or fairly large relative to the overall hook size. Most hook eyes are round, but they can be oval shaped, needle eye like, open with a small gap where it loops back to the shaft of the hook or closed where it touches the shaft. (Note, be careful with open eye hooks, your knot loop can slip through the gap and the hook come off your line.) Hooks eyes can be spade shaped without a hole in them. These are usually used for snelling hooks, a method of attaching the hook to the line by wrapping the line around the shank of the hook. They can also be tapered or ringed and can even be a swivel eye.
Hook eyes can be lined up with the shaft and point or at a 90 degree angle to it. The ones that are at a 90 degree angle to the shaft can be straight out on it or angled. Each has its uses.
The shank of the hook runs from the eye to where it starts to bend back around to the point. Some hooks are long shanked, with a straight shank running several times the length of the gap between the hook eye and the outside of the bend. Some are short shanked with not much distance between the eye of the hook down to opposite of the point. The shank can be straight or bent in a curve away from the hook point. It can also be offset, with a short straight section at the eye, a 90 degree bend to form a right angle then another 90 degree bend back toward the end of the hook. These are usually used for plastic worm fishing and keep the head of the worm from sliding down the shaft.
The distance between the hook point and the shank is the gap. It can vary greatly in different size hooks and wide gap hooks have a curved shank that bends away from the eye so the gap is more than it would be with a straight shank. The gap is very important relating to hooking fish and also using live bait. Live bait like minnows need a wide enough gap to allow them to swim when hooked throught the back or tail, and too small a gap will make it hard to hook bigger fish. Too big a gap will make it harder for smaller fish to take the bait into their mouth.
The rounded part of the hook where the shank bends around to the point of the hook. Most bends are smoothly rounded but some styles have squared off edges and others straighten out quickly so there is less rounded bend to give when setting the hook. Teh flattened bend also is good for fishing some baits like soft jeakbaits like the Zoom Fluke.(compare prices)
Circle hooks have a very round bend including some of the shaft and the point of the hook is angled back toward the shaft. It is made for very specific kinds of fishing.
The distance between a straight line from the hook point to the shaft and the outside bend of the hook. A deeper throat allows deeper penetration of the hook so a more shallow throat would be better for catch and release fishing.
Most hooks have a small splinter of metal at an angle below and pointing away from the point of the hook. This is designed to penetrate the flesh of the fish's mouth and not pull back out easily. Barbless hooks are made for catch and release fishing and are required on some waters like in Yellowstone Park.
Some hooks have barbs on the shaft of the hook, too, and those are used to hold bait in place. Some plastic worm hooks have these barbs but they are more common for holding live bait on the shaft of the hook.
Before choosing your hooks, be sure you know these parts so you can find the right one for your type fishing.