give me a run for my money

It could mean that when someone wants to challenge you, you have the balls to fight back, or to keep up the pace and become, either a winner, or prove them wrong for having the tendency to challenge you. Its a term that firstly was announced of game horses and meant that this horse that I'm counting on can give me my money back, cause I simply have big hopes and expectations from it. Usually this phrase has a lot of different meanings but this one is the most concrete.