Skype will offer everyone who downloads their PC client to install a browser extension Yandex Bar. Yandex Bar, in exchange, will display Skype account balance and provide an easy way to top up Skype account via Yandex Money. This looks like a good way for Yandex to attract more users and possibly regain the market share that they lost to Google last year. In 2011 Skype showed 40% increase in Russian user base ending the year with 22,4 million registered accounts.
So what does Skype get in return? From what I read today it is very unclear: Skype will be promoted on Yandex sites and properties (which is of course a lot of traffic), but it is not specified how.