CCI (or, more formally, NCCI) stands for "National Correct Coding Initiative." This is a project of the CMS (Centers for Medicare and Medicaid) intended to clarify the rules for what procedures can be billed together on the same claim.
Although its scope has expanded a bit, it helps identify "bundled" procedures. One procedure is considered "bundled" in another procedure if paying for that other one includes payment for the "bundled" one. Attempting to bill for the "bundled" procedure results in a denial due to an "unbundling error."
Some NCCI edits put other constraints on reporting two procedures on the same claim, but allow them to be billed with a modifier. The modifier, of course, may only be used if supported by the patient's chart.
Closely associated with NCCI edits are MUE's, which stand for "Medically Unlikely Edits." Typically, they describe maximum doses of medication, or maximum repetitions of the same procedure. For example, there are only so many times your appendix can be removed!
The Claim Scrubber verifies compliance with both NCCI edits and MUE's.