Agile and CMMI

First, Agile and CMMI are not in the same or opposite fields to be compared. Hundred of companies worldwide are said to have adopted an agile practice and got certified the CMMI accreditation.
Second, to define both...CMMI stands for Capability Maturity Model Integration (which is by definition of the SEI) "is a process improvement approach that provides organizations with the essential elements of effective processes". But in a nutshell it boils down to three main components: Generic goals, specific goals and documents to guide the organization to reach an effective process, which on the other hand means a set of deliverables to be available on hand before the time of appraisal for the accreditation.
An agile practice has a lower scope as it mainly focuses on the project management rather than the organization effectiveness; it looks for the work to be done as “the finished work is the measure of quality”. So in a sense, the agile practices can be utilized in a way of practicing of the process guided by the CMMI standards.
Hence, CMMI and an agile practice can really work side by side if the team applying it had the enough knowledge and will.