I was surprised to find that my newly earned reputation points in this community don't seem to carry over to other communities. And I just don't see the point in this. It's kind of like having to go for a new driving examination every time you arrive at a new city. You shouldn't have to prove yourself repeatedly.
Reputation does carry over in a certain way: reaching 200 points on one site gets you +100 on every site. (This is why I have 101 here, for example.) Reaching the level of 200 is earning a universal driver's license. With 100 points one is exempt from new user restrictions, (such as a limit on the number of links in a post) and is able to comment anywhere and participate on meta.
Beyond that, reputation crosses into moderation abilities: editing posts by other users, closing their questions, deleting their questions and answers. It would not make sense to grant such privileges on a programming site on the basis of user's contributions to a cooking site, or the other way around.
Adding to the other answer, reputation is supposed to show how much of an expert you are on the topic of the site - which is why you get past the new user restrictions on other sites, but not all reputation.