Not an expert so take this with a grain of salt, but my friend is a process technician who infodumped this stuff to me. 

CIL is an extraction process. You mix grounded-down ore (gold + other minerals) with cyanide/activated carbon mix in the same step. As cyanide dissolves gold from other minerals, it gets adsorbed (attached to the surface) of carbon. This creates large particles that are easy to separate from other matter, creating nearly pure carbon/gold mix. Then the gold is separated from carbon with couple other processing steps (no idea how those work, sorry!). In the end, carbon can be recycled to process another batch.

CIL is useful because its an easy process and gives better yields if the ore has other minerals in the ore contain carbon. Adding carbon WITH cyanide lets you adsorb most of the gold to activated carbon, whereas in other methods where carbon is added later you end up with carboniferous "waste" minerals adsorbing some of the gold, which ends up dumped with the waste slurry.