Can someone explain Possessive Quantifiers to me? (Regular Expressions)

Perhaps the best place to start is Regex Tutorial - Possessive Quantifiers:

When discussing the repetition operators or quantifiers, I explained the difference between greedy and lazy repetition. Greediness and laziness determine the order in which the regex engine tries the possible permutations of the regex pattern. A greedy quantifier will first try to repeat the token as many times as possible, and gradually give up matches as the engine backtracks to find an overall match. A lazy quantifier will first repeat the token as few times as required, and gradually expand the match as the engine backtracks through the regex to find an overall match.

Possessive quantifiers are a way to prevent the regex engine from trying all permutations. This is primarily useful for performance reasons. You can also use possessive quantifiers to eliminate certain matches.