Low voltage lighting is normally specified for two primary purposes;
1. The fixtures are generally smaller
2. There is a wider variety of beam spreads in the bulbs available
The reason smaller fixtures are possible is simple. Since the filament in the bulb only has to be able to carry 12 volts instead of 120 volts, it can be made much smaller, perhaps 1/4" long instead of 1" long for a 120 volt bulb. Since the filament is smaller, the glass bulb around it can be made smaller, and therefore the fixture can also be designed to be smaller. This is almost always purely an aesthetic consideration, but sometimes space is tight and a smaller fixture is all that will do.
The reason more beam spreads are available in a low voltage bulb is because a small filament can be aimed much more accurately than a larger one. For applications where you are trying to point light at a specific spot, such as a wall graphic or a small table, this may be important. When trying to direct a beam of light in a specific direction, either the bulb or the fixture will contain a reflector. The light created at the filament bounces off the reflector and goes in the direction it is pointed. If the glowing filament is very small, the engineers can very precisely design reflectors to position the light beam. With a larger filament, it is easy to end up with light beams going all over the place.
That's not to say there is no control over higher voltage bulbs and fixtures. There are theatrical spotlights, for example, with amazingly tight beam spreads. Generally though, these types of lights will be used in much larger scale applications, where great distances are involved, or less precision is required.
Next, we should talk about halogen lighting. Many people seem to be under the impression that "halogen" and "low voltage" are synonymous. This is not the case. Halogen merely refers to a light bulb design that uses a halogen gas inside the glass "bulb" that allows the filament to burn brighter (and hotter!), as well as last longer and be a little more efficient. The light from these bulbs is whiter than normal incandescent bulbs.
There are many types of bulbs that are now being produced as halogen, both in low voltage and "line voltage" (120-130 volts). Also, there is a fairly new type of bulb that uses a xenon gas instead of halogen. These bulbs bridge the gap between regular incandescent and halogen. The xenon burns with less heat than the halogen, but is whiter than incandescent. There are still only a few styles of these bulbs available.
Standard household electricity in the USA is referred to as "line voltage". This is normally 120 volts, but can vary between110 volts and 130 volts. (Standard household bulbs are designed to operate at 120 volts. So-called "long life" bulbs can withstand 130 volt current. They burn a little dimmer when the electricity really is 120 volts, but then when you turn your TV off and there is a little voltage spike to 130, they won't burn out.) "Low voltage" technically refers to anything less than this, but usually means 12 volts. There are 24 volt systems available, but the bulbs are still a little hard to find.
Since 120 volts is standard, if you want to use a 12 volt lighting system, you are going need a transformer to convert the voltage. This is often a significant part of the cost of a low voltage system.
There are many different "sizes" of transformers available. You can get a small transformer to run a single light, or a giant transformer to run a lot of lights. Once you have specified a 12 volt system, then you will need to know how many total watts you want to run through each transformer. You can do this simply by adding up the wattage of all the bulbs on each circuit. For example, let's say you want to run four lights at 50 watts each on a circuit. 4 x 50 = 200 total watts. So you would need a transformer that is rated for at least 200 watts.
There are certain wattage ratings for transformers that have become somewhat standardized, so you may not be able to find a transformer rated at exactly 200 watts. Just pick the next size up that is available. Some of the most common sizes are; 60 watt, 75 watt, 100 watt, 150 watt, 250 watt, and 300 watt.
There are a couple of other things to consider about transformers. First, I would like to mention "de-rating". Transformers are only supposed to be run at 80% of their capacity. So if you had 100 watts of lights to run, you should get a transformer rated for at least 120 watts. Having said that, most major manufacturers have already "de-rated" their transformers. So when Juno, for example, claims their transformer is rated for 150 watts, you can run the entire 150 watts worth of lights through it. Since not all manufacturers do this, it is important to communicate the total wattage you want to run through each transformer to your vendor, so that they (we!) can make sure you get the correct transformer.
This "de-rating" is partly due to the fact that the transformers are not 100% efficient. Some of the capacity of the transformer is used up in it's "transforming" function, and some is wasted as heat.
The next item to be aware of are special wiring requirements for low voltage, which simply means that you should plan to use thicker wire than you would for a regular line voltage system. Here's the reason, if you want to know;
Voltage can be thought of as the pressure pushing the electricity through the wire. 120 volts is a lot more pressure than 12 volts. Therefore, you can push the electricity a lot farther with 120 volts than you can with 12 volts. Wires are not perfect conductors; there is some resistance to allowing the electricity to go through. With 12 volts, you can really only expect the electricity to go about 40 feet before it starts petering out. This will result in the bulbs farther away from the transformer being dimmer than the ones that are closer. In order to minimize this problem, you should use thicker wires for low voltage than you would for regular line voltage. Click here to see more information about wires. For short distances (under 20 ft.) 16 gauge wire is usually sufficient. This could be normal lamp cord. 14 gauge is better, and 12 gauge even better. If you have to run your wires 30 or 40 ft, you might even consider 10 gauge wire, which is THICK.