To remarry is to get married again, after already having been married at least once. Your uncle might remarry at the age of 85, after fifty years of bachelorhood.
Anyone who's been married in the past remarries when they do it again. Some marriages end in divorce, and others end when one of the spouses dies. Even if being married didn't agree with them the first time, many people do decide to remarry. The verb dates from the 1520s, formed by adding re-, or "again," to marry, which originally meant just "to give in marriage," from a Latin root.