A basic drive is "6 pulse" meaning there are 6 diodes on the front end bridge rectifier used to convert the AC to DC. If you want to reduce the current harmonics imposed on the line side supply, you can have 2x6 Pulse front ends in parallel (12 pulse), one supplied by a Delta-Y transformer to create a phase shift on the AC side between the 2 rectifiers, which makes a large percentage of the current harmonics cancel each other out. If you want even further reduction of harmonics, you can do it again and have 18 pulse, even 24 pulse in extreme cases.
jraef has described the difference between 6 and 12 (and higher) pulse rectifiers. By supplying a rectifier with higher phase counts (via suitable transformers) you can increase the number of current pulses that the rectifier draws from the supply, improving power factor.
But VSDs have both a rectifier input stage and an switching output stage, and the term 6 pulse, 12 pulse, etc can apply to the output stage.
The earliest VSD devices were termed 6 step or 6 pulse devices. They had 6 thyristor type devices arranged to connect current from the DC bus to the AC output terminals. Each thyristor would drive a single phase terminal, and could only drive that terminal positive or negative, and could only supply a single pulse of current for a third of the AC cycle. If you examined the current applied to a given motor phase, you would see that the AC cycle was approximated by six distinct steps, a very poor approximation with lots of harmonics.
Higher step devices used more complex commutation circuits to turn the switching elements on and off more rapidly than the output frequency, resulting in a greater number of steps in the output and higher fidelity synthesis of the desired output AC.