A split phase motor is a motor with two separate sets of windings, and a means to switch between them.
An electric motor produces 100% torque at 0 RPM, and this is also when the motor draws the most power. In order for a motor to start turning when it is connected to a load, it needs a "kick". This comes from a set of windings called the starter windings. They are designed to draw a large amount of current through the motor, and also from a capacitor, to get the motor running. As soon as the motor reaches a set RPM, a set of swinging weights swing open due to the centripetal force, and activate a set of mechanical contacts that disconnects the starter windings, and switches over to the run windings. The "run" windings are designed to draw less current, and provide less torque, but can run at a 100% duty cycle without overheating.
You often find split phase motors on compressors, or really in any application where there is a large load that needs to get a kick to start.
Split phase motors are easy to identify at a glance because they usually have a capacitor housing right on the motor itself.
A little more from wikipedia:
There are five basic types of competing small induction motor: single-phase capacitor-start, capacitor-run, split-phase and shaded-pole types, and small polyphase induction motors.
A single-phase induction motor requires separate starting circuitry to provide a rotated field to the motor. The normal running windings within such a single-phase motor can cause the rotor to turn in either direction, so the starting circuit determines the operating direction.
In certain smaller single-phase motors, starting is done by mean of a shaded pole with a copper wire turn around part of the pole. The current induced in this turn lags behind the supply current, creating a delayed magnetic field around the shaded part of the pole face. This imparts sufficient rotational field energy to start the motor. These motors are typically used in applications such as desk fans and record players, as the required starting torque is low, and the low efficiency is tolerable relative to the reduced cost of the motor and starting method compared to other AC motor designs.
Larger single phase motors have a second stator winding fed with out-of-phase current; such currents may be created by feeding the winding through a capacitor or having it have different values of inductance and resistance from the main winding. In some designs, the second winding is disconnected once the motor is up to speed, usually either by a centrifugal switch acting on weights on the motor shaft or a thermistor which heats up and increases its resistance, reducing the current through the second winding to an insignificant level. Other designs keep the second winding on when running, improving torque.
Self-starting polyphase induction motors produce torque even at standstill. Available cage induction motor starting methods include direct-on-line starting, reduced-voltage reactor or auto-transformer starting, star-delta starting or, increasingly, new solid-state soft assemblies and, of course, VFDs.
Polyphase motors have rotor bars shaped to give different speed-torque characteristics. The current distribution within the rotor bars varies depending on the frequency of the induced current. At standstill, the rotor current is the same frequency as the stator current, and tends to travel at the outermost parts of the cage rotor bars (by skin effect). The different bar shapes can give usefully different speed-torque characteristics as well as some control over the inrush current at startup.
In wound rotor motors, rotor circuit connection through slip rings to external resistances allows change of speed-torque characteristics for acceleration control and speed control purposes.