Why should an unresponsive victim be placed on the side?

Its called the lateral recumbent position or recovery position. If they are placed on their side, assuming they have a pulse and patent (open) airway, then they wont choke on their tounge or vomit.

Positioning them on their side also prevents the abdomen from squishing the organs.

If a spinal injury is suspected they need to be kept supine (on their back) and suction will have to be used to clear an airway.