The definition of Space Vector PWM (SVPWM)

SV-PWM is actually just a modulation algorithm which translates phase voltage (phase to neutral) references, coming from the controller, into modulation times/duty-cycles to be applied to the PWM peripheral.
It is a general technique for any three-phase load, although it has been developed for motor control.
SV-PWM maximizes DC bus voltage exploitation and uses the "nearest" vectors, which translates into a minimization of the harmonic content.

The classical application of SV-PWM is vector motor control, which is based on the control of currents' projection on two orthogonal coordinates (direct and quadrature, dq), called Field Oriented Control (FOC). For induction machines, the most common choices for the direct axis is to align it to the rotor field (rotor FOC) or to the stator field (stator FOC).

The basic concept is that with a known motor and known voltage output pulses you can accurately determine rotor slip by monitoring current and phase shift. The controller can then modify the PWM "sine" wave shape, frequency or amplitude to achieve the desired result.

For example the desired speed is 200 rpm and the control senses there is 2 rpm of slip so it increases the frequency slightly to bring the speed up. Since torque can also be determined it can also be controlled.

SVPWM just does a lot of sampling, calculating and wave form manipulation. The specific algorithms and deciding what the best output solution is for different situations could fill up several books.

SV means space vector, as in space vector modulation. SVM basically allows a 3-phase bridge PWM drive to supply about 15% higher peak voltage to a motor than the standard sine-triangle modulation scheme by allowing the neutral point of the motor to move away from the nominal 1/2 of the supply rail (it will look like a triangle wave). The characteristic voltage output of an SVM-modulated sine wave is a sine wave with a double-hump on the peaks.

To be more precise, SVM output about 15% more "non over-modulated" voltage than the traditional carrier based PWM. That is the maximum voltage before over-modulation happens. The shape of the phase voltage has a double-hump as mentioned (similar to a standard PWM + third harmonic addition). The line-to-line voltage will not show the humps though.
See a space vector control drive here.