The Spincasting Reel (Closed Faced)
The spincasting reel is the most basic type of fishing reel, and is the type that most young fishermen start with. This reel is completely enclosed in a housing with a small hole at the end of it, from which the line plays out. There is a spindle inside the housing that holds the line, and there is a trigger on the backside of the reel that looses the line for casting. This type of reel is a favorite for beginners because it doesn't tangle easily, and it casts very easily. The one major drawback of the spincasting reel is that it does not cast as far as some of the other fishing reel designs.

Spinning Reel (Open Faced)
The spinning reel is the next most common type of fishing reel. You’ll notice this style by its “open face.” This means the reel is open and not closed like the spin caster. You can literally see a spool of string with a wire bail (loop) over the top. By holding back a trigger switch or the wire bail by hand, you can cast with this reel much farther. Once your timing becomes perfect, you won’t have to worry about the familiar “bird’s nest” that occur when these reels are used improperly. Because the string is housed on the spool, you can cast quite a ways father than the closed-face variety. If you use a 10 to 15 lbs test line, you can play and land some big bass with these. If you like lures rather than live bait, these reels will keep the fun spinning.

Bait Casting Reel
Let me begin by stating that I do not suggest this type for your first reel. Maybe your third or forth once you're proficient with the other two reel types. It is the most difficult to cast with, but it comes in widest variety of sizes, and can handle a lot of abuse day in and day out. There are models for light-weight use, and bigger models for catching huge fish such as Marlin. Baitcasting is used anytime heavy cover is going to be targeted. It's ability to handle heavy line, lures and fish is unmatched as is its strength to weight ratio. Baitcast equipment is NOT meant to be used with light lures; anything under ¼ oz. would be better fished with spinning tackle. Baitcasting tackle is the goto tackle when big fish and big lures meet thick, nasty cover. Also, because you control the cast with your thumb, pinpoint accuracy is possible. Once you become proficient with a baitcast reel, it's possible to drop a lure in a 6-inch circle at 50 feet, with hardly a ripple on the water. That kind of accuracy and "touch" is rarely possible with spincasting or spinning tackle. Baitcasting rods too come in varying lengths and look somewhat like a spincasting rod. But that's where all similarity ends. Baitcasting rods typically have a lot more backbone than the other types of rods. It's this backbone that allows you to muscle a fish from thick weed growth or away from timber. It's also this backbone that allows you to cast heavyweight lures, work big jerkbaits and twitch crankbaits effectively. Try these tactics with most spinning tackle and you'll be exhausted.
The Bait caster Reel mounts to the top of a bait casting rod (this has smaller guides attached to the top side of the rod). This has more uses than the spinning combo - but requires more coordination to use. The line comes off these reels from the top, so it doesn't twist, however, the angler's thumb is used to help control the speed the line unwinds off the reel when casting. Basically, if you forget to put your thumb down over the line on the reel, or don't use enough pressure, the reel spins faster than the line can go through the guides, so it creates a big mess of snarled, tangled line called a backlash, or a "woof" or various other descriptive names.