Master Profile - it means that a curator is overseeing that profile. There are different reasons to MP a profile, such as (1) it's a famous person; (2) it's a profile that gets confused with other profiles and needs to have the fields locked and a Curator's Note; (3) it's a nearly complete, well narrated profiles, with sources and images attached; (4) there are many duplicates and more duplicates all the time and this profile has been chosen to be the one that the duplicates are merged into.
There is a pinned public discussion for asking for a profile to be made into a Master Profile.
The data fields (name, DOB, POB, etc.) can be locked on MPs by curators and unlocked as needed, again by curators. There are curators all over the globe, worked at any hour, so it's not a bad idea to MP ancestors once you have gotten their profiles in good shape with the Overview (About) done and the basic information researched and ideally with sources attached.