Entity that defines and regulates the conditions of assignment and use of domain names, applying to each particular TLD.
The Trustee authority for generic TLDs is ICANN : a non-profit corporation that, for historical reasons, reports to the U.S. Department of Commerce.
As for the national TLDs, each government appoints a Trustee authority with its own rules. For instance, DNS BE is the Trustee authority for the .BE TLD (Belgium); AFNIC is the Trustee authority for the .FR (France).
The registration conditions are set by these entities, and change from one TLD to another. Some TLDs can be more flexible and easier to obtain than others, in terms of restrictions, procedures and prices.