Grow lights are just lights used for growing plants. A grow light can be as simple as an incandescent light bulb that fits in a standard socket, a fluorescent or a High Intensity Discharge (HID) system.
Incandescent lamps are the least expensive and cost about $5 for a good 150 watt grow bulb. You can get one of these lamps from a hardware store or large nursery. If you need a nice looking fixture that can get a bit more expensive. A lamp like this will keep a small house plant growing.
Fluorescent lamps work great for starting seeds or cuttings. The 4 foot size is the most common for gardening. One fixture with 2 lamps in it can cover 2, 10x20 inch trays and get your seedlings ready for transplant. Fluorescent lamps need a ballast to operate; it's almost always built-in to the fixture. The 2 lamp "shop light" fixtures available at the hardware store will cost you about $10. You'll find a wide range of lamps to choose from, try some cool whites, there inexpensive and work well.
High Intensity Discharge lamps are for serious growing. They are very bright and very efficient. One 1000 watt HID lamp can produce the same amount of light as fifty 40 watt fluorescent lamps. All that power in one fixture! HID systems can be divided into a few categories, High Pressure Sodium, Metal Halide, Low Pressure Sodium and Mercury Vapor. The only ones useful for gardening are High Pressure Sodium (HPS or "Sodium") and Metal Halide (MH or "Halide"). The most commonly used sizes are 400 and 1000 watt. The 400 can supply enough light for a growing area of about 16 square feet or a 4 x 4 garden. The 1000 can cover an area of about 7 x 7. For fast growth, figure about 25 watts of HID light per square foot.
Halide lights emit a blue-white color of light, good for leafy growth. Sodium lights emit a yellow-orange color, good for flowering plants. If you're planning on getting only one light, a halide is probably the best choice. If you already have some fluorescents, a sodium may be a better choice. A sodium running with fluorescents in the same area will make the best combination of light spectrum, better than just a halide.