Texas A&M claim to have coined the term in 1922. The coach of the football team was short of one substitute, and addressed a former player who was in attendance in the stands, and asked if he could sit in. The guy said okay, and even though he didn't come into action, the term represents the willingness of the Fans to step in and help their team as substitutes, since only 11 players are permitted on the field.
In this case, In the Netherlands, De Twaalfde Man refers to the club supporters of PSV Eindhoven, a professional Dutch football team. The number 12 is a retired shirt number at PSV, and is reserved for the Fans in the stadium who are all collectively referred to as The Twelfth Man.