This refers to a clergyman getting "ordained" or becoming an official clergyman. Edmund, of course, gets ordained in the book and his career choice is a major point of conflict between him and Mary, his love interest for much of the novel. Being ordained signals a certain kind of lifestyle and belief system that we see emerge in the debates that Edmund and Mary have about the church and about organized religion. Mary has a very cynical view of religion. This greatly contrasts with the pious Edmund, who sees religion as a good thing and has a strict view of morality.
Organized religion, and the politics that surrounded religion in this time period, are one of the major concerns of the book. There were lots of debates going on in this period about how the Church of England should be run, what the role of clergymen should be, how clergymen should do their jobs, and so on. Ordination and religion are tied to issues of reform and "improvement" in the novel as well, and this focus on organized religion makes this book one of Austen's most clearly political.