Speed and flexibility for the most part. Cyanogen has a wiki that goes into detail here:
What is CyanogenMod - CyanogenMod Wiki
with a full feature set here:
Features - CyanogenMod Wiki
Naturally this is an 'unofficial' cyanogen ROM so the feature set is probably incomplete, and some features you may never use.
If nothing else, I recommend rooting and romming your phone just to remove the software you don't use, speed up the device, and make it 'yours'.
The disadvantages can be a less stable phone and a now useless warranty, though I weigh the advantages pretty heavily in favor.