A split outlet is a duplex outlet, or receptacle, with one outlet that has power all the time and one outlet that is controlled by a switch. If you have a bedroom that has no overhead light, chances are at least one of the receptacles in the room is a split receptacle. In fact, this is required by the National Electrical Code (that is, for bedrooms with no overhead light). The idea is that you can plug a lamp into the switched half of the outlet and control it with a switch by the door, so you don't have to walk through a dark room to turn on the lamp.
Most split receptacles are fed by a single circuit, but it's possible to wire a receptacle to be fed by two different circuits, as is often done with a single receptacle serving a dishwasher and garbage disposer.
How to "Split" a Receptacle
Standard duplex receptacles have two halves (each with a set of slots for a plug), and each half has a hot and a neutral wire terminal. The two halves are joined electrically by metal strips, called connecting tabs. When the tabs are intact -- as they are when they come from the factory -- you can connect one hot wire to either hot terminal and connect one neutral wire to either neutral terminal, and both halves receive power. To convert the receptacle to a split duplex receptacle (also called a split-tab receptacle), you simply break off the tab between the hot terminals. This is easy to do with needlenose pliers.
With the tab removed, you must connect a different hot wire to each of the hot terminals to supply power to both halves of the receptacle.
Because the neutral tab remains intact, you can connect a single neutral wire to either neutral terminal, so that the two outlets share a neutral. However, with some configurations, an additional neutral wire is used as a hot wire for the switch; in this case, the neutral should be labeled with a band of black or red tape, indicating that it is hot.
Spit Receptacle Wiring
In the standard wiring configuration for a split receptacle, two-wire cable (with a hot, neutral and ground) supplies power to the switch or receptacle, and 3-wire cable is used between the switch and the receptacle. Again, the tab between the hot terminals on the receptacle is removed. The black and red hot wires of the 3-wire cable each connect to one of the terminals on the switch (always a single-pole switch) and to one of the hot terminals on the receptacle (that is, one hot wire to one hot terminal on each device). The white neutral wire from the 3-wire cable connects only to the receptacle (neutrals don't connect to switches). The ground wire connects to both devices, and to the electrical boxes if they are metal.
Split Receptacle with Two Circuits
As mentioned, a receptacle can be split and receive power from two circuits. Either circuit can be switched or not switched, as applicable. The receptacle can be wired with a single 3-wire cable so that the neutral serves both circuits. The black and red hot wires of the cable each connect to one of the hot terminals on the receptacle.
The important thing to remember is that the two circuits must be protected by one double-pole breaker in the service panel (breaker box).
Here's why: If you connected each of the circuit's hot wires to a different single-pole breaker, you (or someone else) might turn off just one of the breakers before working on the receptacle. This would leave half of the receptacle live; a very dangerous situation. By connecting both hots to a double-pole breaker, you can't shut off one circuit without shutting off the other.