To marry someone is to make an official, ceremonial commitment to be partners. You can marry someone in a church, barefoot on a beach, or in a courthouse.
Some people marry their long-time sweethearts, while others abruptly choose to marry after knowing each other briefly. The officiant who leads the wedding ceremony, whether they're a judge or an ordained minister who's also an Elvis impersonator, is the person who marries the happy couple. The Latin root is maritare, "to wed or marry," and also "to give in marriage."