Proxy Fight
  
See: Proxy.
"Proxy" = approximation of vote, or voting rights.
When you have someone's proxy, you have their right to vote their shares on their behalf. So when there's a proxy fight, there's a "war" of common stock votes. The common elects the Board. When there's a fight, it usually means that half the holders want one outcome as driven by the board, and the other half want another. So they fight, warring on numbers of votes.
Usually, a huge portion of common shares never vote in a board election, but in cases where there's a fight about it, a big number do. They get calls at home, pushing them to vote one way or another.
It's a fight, a la Wall Street. Fisticuffs thrown as proxy votes.