"Represent" is a very slang way of saying they are representing their town. It's actually "representing" but it is usually pronounced "representin". Another slang version of this is "in the house". For example, "where are you from?" "New Jersey in the house" or "New Jersey, representin'". It's not something you would normally use in a conversation. "Beyond"- the way I have heard this used, is that it is used to emphasize what was just said so it can mean super cool, frustrating, annoying, etc. For example, if someone is talking about an annoying customer, they might say "she was beyond" which, in this case would mean "beyond annoying". But, if someone is talking about a great concert they went to and said it was "beyond" that would mean it was "beyond cool". So it basically reflects back the context of the conversation. Again, this is very slang and is something you would use with friends or in a fun way. Not in a formal or professional conversation.

The "represent," is just a short form of "I represent (whatever the area of the country they come from is)." They are trying to say that they are proud of where they come from, I think. I have never heard of "Beyond!" as a saying. It may be a purely American thing. It's possible that it might be short for "Beyond belief," which would be another way of saying "Can you believe it?"