Like most things in history there isn't one "right" answer and there a multitude of changing attitudes throughout the period that Russia was expanding.

There was a huge push for land for additional furs. And really that is the economic reason for the vast expansion into Siberia and even later into Alaska. This would be the economic reason, and it started way back into the time of Novgorod (before even the Mongols). There was also a power vacuum in the East that led Russia to begin to conquer the East. After the fall of the Mongol Empire there was no real power or governance of Siberia. There was of course indigenous people, however they were not unified in such a way to be a threat to Russian explorers. Additionally the Russian method of expansion left the indigenous people alone and used them as trading outlets with a series of forts along the southern Siberian border.

Now, to tie it kind of together. Russia expanded eastwards because, really, it could, without much hardship. It established trading centers to increase production of furs that was then traded back in Europe and also in Asia. The power vacuum leftover by the Mongols and no real unified indigenous people let Russia continue doing this until reaching Alaska.