Well, the simplicity of the rep system's been explained well enough, but in relation to these questions:
"If everybody's giving me negative reputation, should I care? Is it putting me in a disadvantageous position on this forum?"
then it might, if the bar below your name is actually red. A poster like azza has a high arse clown credibility, even by those who haven't seen him post, simply because his reputation is always in the negative. As for restrictions or anything of that sort, then nah - it's not really taken that seriously