How do I enable a profile to be able to mass update records of a specific object in Salesforce?
This is all done through normal object permissions that can be set on the profile or as a permission set. It is important to remember that the user will need to have access to the records through the sharing model to be able to update them, otherwise they will not have access to those specific records. The easiest way to ensure they have access to every record of that object is to just give them Modify All access. This has several downsides to it in terms of security however so please be aware of that.
Overall, it is really just a combination of your object permissions and sharing model.