Anyone can upvote submissions and comments. Every upvote helps float the item higher, and counts for the submitter or commenter as a point of karma.

People with enough karma (currently 500 points) can also downvote (with a few exceptions). Downvotes are pretty much the opposite of upvotes, floating the item lower, and taking karma from the commenter.

The exceptions to downvotes are that you can't downvote:

* A submission.

* A reply to a comment you made

* A reply to a submission you made

* Something that's really old

Did you check out the FAQ before asking? There's a link to it at the bottom of (very nearly) every page: http://ycombinator.com/newsfaq.html

There it says:

    Why don't I see down arrows?

    There are no down arrows on submissions.
    They only appear on comments after users
    reach a certain karma threshold.

(although I see someone else has already quoted that)