1. Larger index Up until a few years ago, Yandex constantly delivered more results for Russian queries than Google. That's particularly important for the long tail queries.
2. Better search results Yandex have concentrated on tackling the specifics of the Russian language from the very beginning and were way ahead of Google, when they decided to start covering that market.
3. Cultural adaption Yandex offers many features that appeal to Russian people. Mikhail mentioned a few, I would also add dictionaries and the virtual keyboard (useful for Russians overseas). Little things count too, e.g.: Фотки instead of Картинки
4. Great design Even with many available features, Yandex doesn't appear crowded (like Yahoo for example). It has a clear-cut design (Go ArtLebedev). I particularly like the inviting example of what to search for underneath the search field. I can just see my grandmother looking at Yandex.ru and knowing what to do, whereas Google would appear to her more like an expert tool.