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When you're logged in to Reddit, you'll be able to upvote and downvote items to help determine their rank. You get one vote per item, but you can change it after it's logged.
The number appearing between the up and down arrows is the submission's score: the number of upvotes minus the number of downvotes.
You may also notice that posts with the highest score do not always rank at the top. This is due to Reddit's time decay algorithm. Posts on the front page are obviously more visible, and therefore have a higher chance of being upvoted. But the site wouldn't be valuable if the same content remained on the front page all day.