You might meet a minister of the religious kind — a pastor or a rector. Or, you may meet a minister of the government kind — a prime minister or a minister of finance, for example.
You don't have to be religious to minister. When you minister to someone, you take care of them. All of these meanings of minister — both as a noun and as a verb — contain a grain of the original Latin meaning, "servant." A minister in a church serves his or her flock, and a prime minister serves his or her country.