WHAT is a mezzanine codec?
A mezzanine or intermediate codec is a codec that is designed for post production. Often called an editing format. These codecs are intraframe-only meaning ever frame is compressed as its own frame.
WHY are these codecs better to edit with?
Lower CPU overhead.
Fully intraframe for easy video scrubbing.
Resilient to generation loss.
Smart rendering. Don't change a frame or have effects rendered on the timeline? That frame is copied to output and not recompressed. This workflow avoids generation loss.
Work with lower quality/lower resolution files saving time to render effects, screener outputs, etc that can add up to hours of project time. Reconnect your edit to the original full res before going to colour.
What do you do with the originals?
Keep them. Storage is cheap in the grand scheme of production and if you're picked up for distribution you will need to furnish your camera originals. You can use low-quality proxies if you plan on onlining your film later on.
Is one of the codecs better than another?
Similar results at similar bitrates/quality levels. ProRes is Apple Products, DNx is Avid, and Cineform is GoPro; Premiere can use any of the three comfortably (it can only read ProRes on Windows.)