The topping lift is actually just a fancy, specialized halyard. It is almost always made of the same material (spectra and kevlar aramid are most popular) as a boat's halyards and has a single-finger release shackle just like a halyard.
So what's the difference? Simple: a halyard is used exclusively for raising a sail, no matter where it is on the boat. The topping lift, however, is used for raising either a spar, the mainsail boom, or the spinnaker pole. Now, there are two major casualties that can happen to any line on a boat. Either it will part, which is analogous to breaking only with a slow unravelling followed by a snapping of the line (line rarely spontaneously breaks because of its spliced construction), or the crew will have to intentionally lose control of the line because it has fouled itself (tangled) with various parts of the ship. This procedure on a halyard is called "skying", which means to free it from any load, then pull on the line until the shackle is at the top of the mast. This prevents the shackle from hurting someone if it comes loose. The bowman will climb the mast later and retrive it. This presents a problem for the bowman- he's now missing one of his halyards, and in a race situation, this means a sail has to be completely dropped and unrigged before the next sail can be raised. That's lost time. So a smart bowman will rig his topping lift to the jib, and simply use the remaining halyard on the spinnaker. Many smaller racing keelboats (the Etchells and Rainbow 24 classes for example) do not have two halyards to simplify the rigging. This means they automatically use the topping lift for the second halyard.
I know that sounds complicated, especially if you've never sailed (let alone raced!)before, but the bottom line is this: there really is no difference between a halyard and a topping lift.
So why do boat makers even bother to put halyards and topping lifts onto boats? It is not necessary to have a topping lift to bring in a sail after lowering it unless you have a "cat rigged" boat. To illustrate why we actually have a topping lift, we need to understand something or two about spinnakers (whip out a sheet of paper). First, draw an equilateral triangle with only one point at the top, and the other two points at the bottom. Congratulations, you master sailmaker, you! You just made your very first spinnaker. Now, we have to attach it to our boat. So now imagine yourself standing just behind the mast of your very own sailboat looking forward. You've got a martini in your hand, and you are enjoying the fact that as a multimillion dollar sailmaker, you can afford to have poor college student/professional sailors like NotFabio do all the bow work.
Oh sorry, I digress.
Anyhow, the two of us have rigged our spinnaker and we're cruising downwind, leaving the rest of the fleet in the wake. You look at the spinnaker and see at the very top, we've attached one line. This is the spinnaker halyard. It runs up from the spinnaker's head to the mast (draw it in!). Now, you look at the bottom of the sail. On the left (port) is a pair of lines (draw these two in too!), one of which has a rubber puck just below the shackle, which is attached to a metal ring on the sail. This line is the guy. The metal ring is called a clew. Attached to the guy, just ahead of the puck is another line. This is called the sheet. The sheet appears to be under tension, while the guy is not under tension. You look back and see that the sheet is currently wrapped around a winch back in the cockpit, but the guy is not. Now you look to the right (starboard) clew and see two lines (draw these in!) but the setup is reversed! On the right, the guy is under tension, and the sheet is not. Furthermore, the rubber puck is pulled tightly against a large metal pole extending from the mast to the starboard side of the boat. This is the spinnaker pole. In fact, it looks a little like the picture at http://www.nadn.navy.mil/SailingTeam/offshore/photos/onboardNA18.JPG
So now, what does each of the lines do? The halyard pulls up on the spinnaker, and keeps it raised. The sheet pulls back on the spinnaker and keeps it open. The guy pulls on the spinnaker pole, which allows us to set an angle with the sail so that the wind is always pointing right into the sail. This lets us sail fast! So by now, you're wondering how the weight of the spinnaker pole is balanced. It is pretty heavy- about 50 pounds, and the spinnaker can't generate that much lift. Furthermore, the spinnaker is a very light fabric, even lighter than silk. If we used the halyard and the spinnaker to support the weight of the pole, the sail would rip. This is where the topping lift comes into play. At the very tip of the pole, there is a line running up, and a line running down. The one running down is simply called a downhaul because it hauls the pole down. The topping lift lifts the pole up. This is starting to make sense. You feel a strange urge to run back to the cockpit and snatch the controls from the hands of NotFabio! This is easy! You're so glad you saw the offer to come sailing with NotFabio on his homenode!
Sorry, I'm mumbling again, aren't I?
Anyhow, what Atlas says is partially true. This rig is more popular on East Coast boats and racing boats. It's faster and allows for more fine tuning of the spinnaker. And it probably is more complicated than a cat rig, if not more expensive. And any good trimmer will tell you there are a million things to trim on a racing yacht. However, it doesn't have to be more impossible for the beginner, and you really don't need one to lower or raise the sails. Furthermore, the topping lift is rarely run backwards. The reason for this is because it's unnecessary. With the halyard providing upwards tension on the mainsail, the outhaul providing backwards tension, and the boom vang and cunningham providing downwards tension, we really don't need a topping lift to control the mainsail. If we want to pull the boom in, we can just use the main sheet to pull the boom in to the centerline of the boat. In the end, it's all a matter of naming conventions however, as the use of a topping lift is the same as any other line, just with a different direction of tension.