People can buy gold (a month of "reddit premium") to thank others for their contributions. In October 2013, they launched the "reddit daily gold goal" bar that displays how much gold is needed every day to pay for all (server?) costs (http://www.redditblog.com/2013/10/thanks-for-gold.html). I don't know if it includes other costs or just server costs actually. I've looked for some statistics over time to see whether the goal is being reached often or not but I can't find a graph.
They've got a couple other revenue sources like merchandising and their own advertisement system. But it would seem Reddit is not a massively profitable business at this point.