You can see hints in this review:
It should be is easy to search the web, enter URLs, open new tabs, save bookmarks etc. All of this can be done with the current browser in SailfishOS. The browser seems to work pretty fast and flawlessly. We heard at the launch event that the rendering engine is Gecko (same as in Firefox) so it is likely to have good support for HTML5 features. However in terms of usability, Chrome for Android is still the best mobile browser we’ve used so far. In particular the SailfishOS browser does not seem to have support for landscape mode. Hopefully while SailfishOS matures, the browser will grow to be more polished as well.
So.. the whole point of this phone is HTML5 apps. Yet Chrome is a more usable browser, and the author is hopeful the native browser "will grow to be more polished as well".
Android apps can be run using Alien Dalvik (probably some sort of virtual machine layer). You can either get both free and paid apps from the bundled Yandex store
No mention at all of the huge problems with this approach: this means no Google Play Services, and it removes all motivation for developers to build native apps: they can just point users at the Android version. (Also, Yandex has an Android store?!)