For example when you enter something in the search box but forget to switch language on your keyboard it will detect it and provide right results with 'did you mean..'.
Also most websites on Runet just sucks. Pages are badly formed with lots of adds and without any SEO and Accessibility in mind. Sometimes when the page does actually contain a relevant information Google will give it a pour pagerank because of pour Signal vs. Noise ratio or because it's far from the top of the page. Poorly formed pages are hard for search engines to deal with but it seems Yandex does a better job (at least in Runet).
Yandex Maps has a Killer feature - you can measure distances with a simple tool. I have no idea why no one else does that!
Another important thing: Google is not faster (if not slower) than Yandex in Russia. That's something which I notice when I compared Yahoo! and Google while I lived there. Yahoo is a little bit slower than Google and when one makes a couple of searches (trying different words and phrases) it becomes really annoying. Yandex doesn't have this problem. Moreover it loaded faster when I used it outside of Moscow in regions with a slower internet connection (may be their datacenter was closer, I don't know).
And if you consider entering the url in the address bar it's even faster to type ya.ru vs. google.com. Of course it's not an issue now when I use browser hotkeys (type 'y search term' or 'g search term') but from my experience there are lots of people who still type the URL.
But the major key to success was a large ad campaign on TV when Runet was really young and small and no one heard about Google yet. I remember the time when I knew about two websites: Yandex and Mail.ru and those two still mean internet to my mom. Yandex became a synonym to 'search' alongside with Rambler. But unlike the later Yandex keeps innovating and it's still ahead of Google which surpassed Rambler last year.
I'm pleased to see that there are countries where Google does not own the market. Unfortunately it’s not the case in Europe where people use it 99% of the time even though there are great local search engines. Competition is great and it’s the only thing that drives the innovation.
It’s really funny when one person says to other 'Just google that' and the other opens Yandex and search but in Russia it’s the usual thing.