Things like "Don't be dissin me" and "yo I was there to represent" really boil down to some of the most important aspects of social behavior.
The whole 'respect' thing .. it's important. Much of social interaction, from my perspective, has to do with how much I respect people and how much they respect me in return. Opening a door for someone, for example, is a sign of respect. Saying "Thank you." when someone does it, is an exchange of that respect. Someone has to make the first move, and when noone does problems arise. Even when I don't want to respect someone, I have to if I want them to respect me. So sometimes I'll do it for that reason alone. Sometimes I find someone who doesn't respect me, and their respect isn't worth anything to me either. That's when I just don't bother, or worse. And it's then that problems crop up. I try to keep that to a minimum though, because it is rare that someones disrespect can be so easily disregarded.
As for 'representing' ... well, that's about being loyal to my friends (pack) or loved ones. Standing up for them when someone says something bad about them. When people know I'm someones mate for instance, if they say something bad about my mate with me around and I don't 'represent' .. then I'm basically affirming their accusations or opinions. On the other end, someone close to me can effectively become a guidewire for hurting me if they don't 'represent' me when something bad is said about me. Especially if I'm there, or if I find out about it later. It's one thing if someone I don't respect says something bad to me. I can ignore it. But if it's done when someone who I do respect is around, and they don't 'represent' me? That hurts. It etches into my own levels of respect, both about myself and about the so-called friend. True friends and packmates don't let that happen. They represent.