OK I am going to try to clear up all of the confusion, so bare with me :)
The reputation system still exists in the same manner it always has. However, the algorithm to calculate rep power (how much influence you have on another member) has been altered so that those of you with a lot of reputation can still feel comfortable posting a negative reputation comment every so often without feeling like you're going to kill the new member. Additionally, previously new members had to have 10 posts before they gained their first point of rep power and now they only need 5 posts. What all this means is that new members will start spreading reputation around sooner and old timers won't be affecting reputation so drastically.
Reputation is used for when you agree or disagree with a post, when you find it helpful, when you have a comment to make about the post that's either good or bad.
Then there's the voting system ...
Every individual post can be up-voted or down-voted. You can only influence a post by +1 or -1 depending on your vote.
If you give reputation to a post, you will automatically up-vote or down-vote the post based on the reputation that you gave.
However, you can also very easily up-vote or down-vote a post by clicking the little button, without having to type anything in or refresh the page. When you do this, you are only affecting the post's vote count by +1 or -1. You aren't affecting reputation.
So let me make sure you guys get this ...
You give reputation. You can leave a comment about the post. You affect the user's reputation based on your own rep power. You automatically increase or decrease the post's vote count by 1.
You just up vote or down vote. You increase or decrease the post's vote count by 1. There is no effect on the user's reputation and the user doesn't know who it was who up voted or down voted them. The idea though is for lots of people to do this and for posts to accumulate lots of votes each.
Unlike reputation, where you would only give rep if you thought the post was helpful, or thought-provoking, or useful, or gave the wrong advice, or you disagreed with it, you would up-vote or down-vote if a post is well-written or uses 1337 speak or doesn't have code tags or does use code tags correct on the first try, etc etc.
The idea is for posts to accumulate lots of upvotes or downvotes (similar to Digg, for example) to the point where when you're browsing a forum listing, you can skim the OP vote counters to see whether a post is even worth clicking into.