I can't go completely in reverse chronological order, or you won't know what's going on.
So to quickly summarize: we were in the "regular" adoption-from-China process. That is, we submitted information on our family along with a request for a child, including the sex (girl) and age range (as young as possible) we hoped for. From that point, we waited for the Chinese government's adoption office (China Center for Adoption Affairs or CCAA) to match us with a child.
Our adoption agency periodically sends out lists of waiting and special needs children. During the time we've been waiting, we have expressed interest of varying degrees in some of these children. A few months ago we were strongly drawn to one of these children, a three year old — Mei Mei. (Names have been changed to protect the innocent.) We requested that she and our family be matched. The agency chose us to be Mei Mei's family!