Originally a
cricket term, the Twelfth Man has been borrowed to describe an aspect of
home advantage in
football N.B. Americans, this is soccer.
A normal football team, like a cricket team, has eleven players (I wonder if there's some significance there?). When a team is playing at its home ground, it is assumed that they have the advantage. Two-leg games use this assumption to motivate the oft-controversial away goals rule; that scoring at home is easier than scoring away.
One reason for this is the Twelfth Man. Inevitably, the home team has more fans in the stadium than the away team. These home fans spur on their team and boo the opposition, and can sometimes add that vital psychological edge that helps one team overcome another. This extra support is what is called the Twelfth Man
Arguably, in much modern football the effect of the Twelfth Man is diminished, as more people travel to away games and crowds are much less rowdy since the abolition of stands. However, some teams like Turkey's Galatasaray, use it to great effect; their stadium is nicknamed simply 'Hell'.