Hi, it means that you have met someone who is equal to your skill/of a higher skill than you. For example if you were a really good chess player and you easily beat all of your opponents. If you then met someone that you struggled to beat then you could say 'I have met my match'

Your match is the person who matches you in skills or abilities. If you have met your match, you have met the person who is your equal or better, and you will not be able to beat them at whatever you are doing. You use this idiom when you are about to lose at something. You have been winning at tennis all week, but you have met your match now that Cindy is playing. I have met my match now, Mark; your grades are higher than mine. (http://www.answers.com/Q/What_is_the_meaning_of_the_idiom_'met_your_match')

It means you have found someone who have your skills or that is more talented than you. (you found someone who is better than you)