Provider is a synonyme with "Supplier" which means:
Someone whose business is to supply a particular service or commodity
Just as in real life, a provider is someone / something that helps you solve communicaiton with a certain service or help you solve a problem.
For instance, the Membership Provider in .NET is used to handle Membership such as Authentication, Registering new Users and many more options comes with this.
The Role Provider goes hand in hand with the above, because it helps you handle Roles attached to users that you have in ( They have Memberships! ).
You might want to read this: Microsoft ASP.NET 2.0 Provider Introduction from MSDN