MRFC stands for Media Resource Function Control and MRFP stands for Media Resource Function Processing.

When CSCF gets INVITE message and find some incompatibility between two phones that want to communicate each other, it passes that information to MRFC. Then MRFC adjust SIP messages so that the call flow through MRFP which perform transcode (translating the codec) from one to another, so that each of the party is just using its own codec but still can communicate with the other party which uses different codec.