Hard to imagine what's in it for Quora. - Network connections? Their CEO is the former CTO of Facebook. - Help with fundraising? They raised $80mm at $900mm valuation not more than a month ago. I strongly suspect Quora is planning a huge pivot which they feel is ambitious but doable in 3 months, and YC believes in the value of this pivot; that is the only plausible explanation I can think of.
Direction probably. Quora has floundered for nearly 5 years, burned millions of dollars and still has a questionable product. Meanwhile Stack Exchange has been around only a year longer, a fraction of the funding, and pretty well owns the entire question-answer niche.
Stack has seven sites getting at least 100,000 visits per day. One is a break out homerun (Stack Overflow obviously), and it drastically dwarfs the other sites. All but a few of their top 20+ sites are strictly technology focused, and the others are geek friendly (math and video games), so they cross over conveniently.
Most of their network is flailing. Photography is 3 years old and gets a whopping seven questions per day - that's what most of their network looks like.
Stack doesn't even remotely own the Q&A category. They own one piece of it, and will never own anything more than that, because they can't translate success in technical Q&A to other categories well. You can beat StackExchange at any given of their smaller niche sites, because they can't do them as well as someone that is dedicated to just that niche - the same reason Quora et al can't compete with Stack Overflow.