Basically they don't make money, from what I understand. Free image hosting is relatively expensive for the host, and because most of the usage is hotlinking (i.e. most of the people using their bandwidth never actually see their site), they lack much ability to make it up by advertising or whatev'. So it's hard to keep up, and that difficulty only gets worse as the site gets more popular and sees more, largely unmonetizable, traffic.
So the cycle for these things is they start small and probably largely easy to use (i.e. there's little to no money making bullshit involved), people start using it, then ease of use degrades as the site owner tries (ineffectively!) to offset the cost of maintaining the servers, and eventually it buckles under the weight of steadily decreasing usability on top of increasing expenses without commensurate increase in income.
... or in other words, capitalism is incapable of being a sustainable system for maintaining free image hosting (which, in fairness, is completely bloody obvious if you think for a few minutes). Expenses increase faster than income and the basic structure of the service is pretty much impossible to effectively monetize in the face of expanding usage. You're probably not going to see an image host that doesn't follow that described cycle until someone or another turns one into a public utility, and it's probably going to be a long, long time before that happens.