LED THEORY 101
AC stands for "alternating current" and DC stands for "direct current". An AC voltage is just a sinusoidally-varying voltage. You can still use Ohm's law with AC voltages and currects. The power delivered to the outlet in your home is an AC voltage, usually around 115VAC or 230VAC depending on where you are in the world . Often you'll want to convert the AC voltage from an outlet to a DC voltage, and that's what a typical DC power supply does. For example, the 12V "wall wart" power supply turns the AC voltage from the outlet to 12VDC. Electricity can be dangerous, especially to power coming from the wall. Make sure you understand and take responsibility for your actions when working with mains electricity.
Power tells us about how much energy we're using in a given amount of time. It's important to figure out whether we have a good enough heatsink, a big enough power supply, or fat enough wires. Power equals voltage times current, or P = I x V. Power is measured in Watts, abbreviated with the letter W. So say you have a high power LED with a 30V forward voltage and a 1A forward current. That means the LED dissipates 30W, and you'd need a power supply greater than 30W to drive it. Some of that power gets turned into light, and some of that power gets turned into heat. While LEDs convert a greater proportion of power to light than, say, incandescent bulbs, they still generate plenty of heat that must be heatsinked.
If you want to build your own LED grow light but don't have experience with electronics, the knowledge you need can be a little intimidating. Luckily, there is only a little bit of electronic theory you need to know to get going. We can't possibly cover everything, but here are some basic concepts to get you started.
VOLTAGE, CURRENT, AND OHM'S LAW
Electricity is all about the flow of electrons to transfer energy. The best way to understand how this works is with the water analogy. Current is like flow; how much electricity is flowing through a circuit, or how much water is flowing through a pipe. Voltage is like pressure; the harder you push, the more flow you get. Resistance limits how much flow you get; a resistor resists the flow of electrons like a skinny pipe resists the flow of water.
Ohm's law is the law for electricity. It's what relates current to voltage and resistance. Specifically, voltage equals current times resistance, or V = I x R.
For a given resistance (measured in Ohms), the more current you'll get (measure in Amperes, or amps) for a given voltage (measured in volts). You might see these units expressed in units like millivolts or milliamps. These are just prefixes that act like multipliers on the units. For example, a milliamp is one one-thousandth of an amp. Volts are abbreviated with the letter V, amps with the letter A, and Ohms with the greek letter Omega.
An electrical circuit is a closed conductive path for electrons to flow. If you connect a wire to both sides of a battery, you've made a circuit. Current flows from the positive side of the battery, through the wire, back into the battery's negative side. (This is called a short circuit. Don't do this).
The most basic electrical circuit is a resistor attached to a voltage source, like a battery. The current through the resistor equals the voltage divided by the resistance, which we know because of Ohm's law. If there are multiple components in a circuit, we can figure out the current and voltage for each part using Kirchoff's laws.
DIODES AND LEDS
Diodes are a type of semiconductor device that only allow current to flow in one direction. In the water analogy, they are the equivalent of a check valve. Diodes have a "forward voltage" that is the minimum voltage that must be applied across them to make them conduct from their positive terminal (Anode) to negative terminal (Cathode). When current flows through the diode, it always has this voltage across it. There are a lot more subtleties of diode behavior and special types of diodes that do specific things, but that's the basic idea. Current flows one way, and there's a voltage drop across it.
LEDs are "light emitting diodes" and, believe it or not, they are a special type of diode that emits light when conducting current. All of those annoying blinking lights on your TV, router, and other gadgets are LEDs. To drive one of these typical LEDs, we add the LED in series with the resistor in the basic electrical circuit descibed above. The current through the resistor and the LED will be the same, so the resistor limits the current through the LED. For a more complete tutorial on driving LEDs this way, check out this tutorial and then come back here.
For horticultural lighting, we're interested in high power LEDs. They draw a lot more current, which means they generate a lot more light and dissipate a lot more power, but they're still LEDs. You could drive them with a DC voltage source and a current-limiting resistor as described in the tutorial linked above, but this wouldn't be very efficient because the power dissipated in the resistor would be high. So instead, we will often drive high power LEDs with a constant-current power supply. Don't worry for now about how these work for now. Just know that you provide a DC or AC voltage to their input, and you get a constant DC current at their output. If you want to drive a high power LED with one, you simply connect the positive side of the LED (Anode) to the positive side of the supply output, and negative to negative. You get the current specified from the power supply, as long as the power supply is capabale of providing that current at the LED's forward voltage. (Remember that power is current times voltage, so high power LEDs often require both high voltage and high current.) More on this later.
"I wanna make a big honkin' LED light," you say, "what's all this have to do with anything?" When you're learning anything technical, it can be overwhelming to read about the theory and difficult to see how it matters. Don't worry, you don't have to remember or even understand it all now. This information provides the basic electronics knowledge you'll need to build an LED grow light, and will serve as a reference for all future discussions. Refer back to this post as needed while we get into more details of designing your grow light.
This is an extremely short introduction to electronics, so if you're interested in the topic you would do well to read something more comprehensive. The best book for beginning electonics is Practical Electronics for Inventors by Paul Scherz. It's cheap, covers a lot of material, and doesn't assume any prior knowledege.