Is there prestige to be had by posting to arXiv? Do people ever upload papers exclusively to arXiv, or do authors simply use arXiv to assist in review while they find a journal to publish in?  If people sometimes publish exclusively on arXiv, what's the point?  What do they get for their work?  A paper on their CV?  Is it at all prestigious?
I suppose some senior people may publish exclusively on arXiv but they are a minority and I can't think of any examples right now. Publishing in mathematics takes a long time. Journal backlogs of multiple years are common enough that if you wait for your paper to appear in print it is already old. This is less of a problem in the other subjects that arXiv covers but still...

So what does publishing on arXiv get the author? Primarily it gives the paper a time stamp and makes it publicly available. Putting up a paper is fast, it only takes a few minutes and it gives a reference number so that you can cite it in a talk or in a paper. Normally you would have to wait until you get page numbers from a journal. And if you are giving a talk on your paper when you have just finished the work that might still be years in the future. 

One interesting feature of publishing on arXiv is that you can write small notes and put those up. You can write the "user's guide" version of a paper. You can post a supplement to a paper that wouldn't be publishable on its own. 

Ultimately what it all boils down to is that people post documents to arXiv that they want other people to see and hopefully read. 

As for prestige, no. There really isn't any as far as I know.