Basically, when you ask a question, (1) Quora suggests a set of users determined algorithmically to better answer your question — that are not among your friends (this is important!) —, and (2) the suggested users have an "answering fee" that they (can?) require in order to answer the respective question.
For the first part:
The first is suggestions for Ask to Answer, a list of people on Quora who can best answer a particular question. We've always offered the ability to ask someone to answer a question, but you had to know about that person ahead of time. Our new suggestions list identifies people who have written good answers to similar questions, so you can discover and ask people you might not otherwise have found.
For the second part:
The second part is credits, a virtual currency that's used to ask people to answer. Everyone on Quora will get a balance of credits, and each person on the new suggestions list has an ask to answer price.
From this Quora thread.