Herbert Brown Maw was born in Ogden, Utah, in 1893 to Emma Brown and Ephraim Goodman Maw. He later moved with his family to Salt Lake City where he attended LDS High School and the University of Utah Law School. He received a master's degree and a doctor of law degree from Northwestern University. During World War I he served as a Mormon chaplain in the military. He married Florence Buehler in 1921, and they had four children.

Maw taught speech and political science at the University of Utah and was dean of men from 1928 to 1936. He served for ten years in the state senate and was senate president for four years. He promoted direct primary elections, old-age assistance programs, and government control of public utilities. A member of the Democratic party's liberal wing, he failed in three attempts to win his party's gubernatorial nomination against conservatives, including Governor Henry Blood, whom he challenged in a bitter convention fight in 1936. When the state's first direct primary was held in 1940, Maw defeated Henry D. Moyle for nomination as governor, and went on to win election as Utah's eighth state governor over Republican Don B. Colton, a former congressman.