I'm considering rooting my Razr M.
If I do that but don't install an alternate ROM, will this erase anything on my phone or simply "unlock it"?
If you need to unlock the bootloader first (I could not find that in the instructions; you might check the script for the term
oem unlock, usually done via
fastboot), this includes a factory-reset, which would mean "all clean up delete", i.e. all data and your self-installed apps would be gone.
Otherwise, if no bootloader-unlock is involved, the rooting process itself would usually not delete anything.