First you need a basic knowledge of electric motor, brushed type with permanent magnet on stator.
Magnet makes an excitation field, while current trough rotor makes a perpendicular magnetic field (they ara so called d-axis and q-axis fields), both toghether produce torque.
When motor spins brushes commutate, so d and q axis field are always perpendicular, so there isn't loose of torque as T=d X q vector product.
Syncronous or induction motors are made in reverse, rotor is a permanent magnet or a cage, stator is switcehd by means of transistors rather than brushes. One important thing is to commutate, so that stator field is perpendicular to rotor field. This is quite easy for permanent magnet motor, using rotor position encoder, but not so easy for induction motor, as magnetic field in cage changes dependant of frequency and load.
If you feed induction motor with normal PWM you have the same picture as it would be powered from mains power, except you can change frequency/voltage.
In space vetor pwm, you compute current in rotor cage by means of a encoder giving speed value, you also need to know voltages on all three phases, phase currents, exact inductance of stator, rotor, resitance, streess flux,...then you are able to compute rotor flux in d and q axis, relative to excitation stator filed. This is passed to pid regulator, that wants to cancell d- component and bring q-component perpendicular to stator field, so computed vectors are transformed in thre phase and currents are injected into stator. You now have a induction motor that works like a syncronous motor or brushed dc motor. This is the goal of that.