An ordained minister is one who's been appointed to the job by a special church authority. If you've ever had to sit through a lecture about the evils of too much TV, you know that a person doesn't need to be ordained in order to preach.
When you say that people have been ordained, you usually mean that they've been invested with special powers. After a priest has been ordained in the Catholic church, he can perform sacraments. Such priests are higher up in the church hierarchy than others, and those below them can be called their “subordinates,” a word also related to ordain.
