At a high level, CQRS is simply separating your reads from your writes. It follows the observation that most web-related DB queries are in the form of reads and much fewer writes. I don't know about solving the CAP theorem, but it does a very nice job of scaling horizontally.
http://cqrsinfo.com/documents/cqrs-introduction/
While making the problem easier, I do not know if this actually "solves" the CAP theorem issues.