The sound is actually a "POP" rather than a "crack".
The sound you hear when a Chiropractor adjusts the spine is called a "cavitation".
When a Chiropractor adjusts a joint, we put a gentle thrust through the spinal joint.
This separates the two joint surfaces and briefly creates a negative pressure within the joint. This pulls the Nitrogen and Carbon dioxide out of a (synovial) fluid state and into a gasseous state which produces the poping sound which is mistaken for a "crack"! You can try this yourself by pressing your palms tightly together then pulkling them apart quickly - did you hear it?