On January 18, 1486, Henry VII married Elizabeth of York, uniting the Houses of Lancaster and York. The symbol that resulted was the Tudor Rose, both red (Lancaster) and white (York). This marrriage was one of the actions Henry took after defeating Richard III at Bosworth Field to establish his rightful claim to the throne. She was the eldest child of Edward IV and Elizabeth Woodville.
Richard III had Parliament declare her parents' marriage null and void and their children illegitimate in 1483, just before he took the throne. After defeating Richard, Henry directed Parliament to repeal that law, strengthening the effectiveness of his marriage to the house of York through Eizabeth.
Accounts indicate that Henry and Elizabeth had a happy arranged marriage, blessed by children, four of whom survived childhood (out of seven): Margaret, Arthur, Mary, and Henry.
I'm reading Giles Tremlett's biography of Catherine of Aragon right now, and after the death of Arthur, the Prince of Wales, Tremlett recounts that Elizabeth hoped to provide Henry with another "spare" heir in 1501-1502. She did become pregnant, but died in February of 1503 after delivering a girl, Katherine, who died the same day she was born, February 2, 1503.