What is an endowed chair exactly? How does it compare to a “normal” position? US universities have a tendency to name chairs after people. Just to give a few examples from Harvard: Hollis Professor of Divinity (love that title), Steven and Maureen Klinsky Professorship of Practice for Leadership and Progress (too long to fit on business card), Carl H. Pforzheimer, Jr. Professor of Teaching and Learning, etc.

I understand that the people whom the chairs are named after are rich and donated money to the school in the past. What I do not understand is in what aspects it changes the nature of the position. Are these chairs more highly regarded that just being "Professor of Divinity" for example? Are they better paid?
Chaired positions are generally endowed, in that the money provided for the salary, and some other benefits (e.g., a dedicated assistant) or increased research funds comes from the interest on principal donated by the person or people the chair is named after, which is part of the school's overall endowment (UC San Diego has a more broad definition, as does Wikipedia). Being named to a chair is a prestigious award, and in many cases it is a lifetime (or at least, until retirement) position. Some chaired positions are given on a rotating basis (e.g., for five years), but nonetheless it is prestigious to be named to an endowed chair.

While it is not strictly true that professors in chaired positions are paid more (because in most cases pay is negotiable), because universities use a combination of pay and incentives such as an endowed chair to lure highly sought-after candidates, the pay is probably on average higher than the average non-chaired full professor would have at the same institution and department.

Finally, some schools use chairs at the university level (versus the departmental or school level) that they dole out throughout the university. The positions can therefore be used as an enabler for some departments with less money to attract particularly important faculty members that they might not have had an opportunity to attract otherwise.

For a specific example of the policy for endowed chairs at one university (Rensselaer Polytechnic Institute), see here.