Russia acquired a huge empire before the Industrial Revolution. The vast area of Siberia provided little commercial opportunities. It didn't have much useful mineral resources, such as the silver mines in Americas or gold mines in South Africa. It didn't even provide good lands for agriculture. The steppe land in Ukraine was more than enough for grain harvest. Russia herself was thinly populated, and a huge empire posed all kinds of problems for administration.
So why did they keep pushing eastwards?
The vast area of Siberia provided little commercial opportunities.
On the contrary. Siberia is home to a large number of animals, which can be hunted for their fur. Russia had a long history of trading fur even before the conquest of Sibera, and fur was a highly prized commodity at the time, so expanding into Siberia to get even more fur to trade made economic sense for Russia. During the same period the fur trade in North America was also starting to grow, because of the high price of fur on the world market.
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.
Originally, as /u/randomhistorian1 pointed out, 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 led 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.
A few other notes: Russia wasn't "thinly" populated in the way we think. It was concentrated in "European Russia" and then was incredibly sparsely populated throughout the rest of the Empire. It was also one of the most populated European country. Especially during the Pre-Modern era.
Also, even though Russia had the best land and a lot of land in the "Black Earth" zone, its agricultural production was abysmal until the Soviet Union. It simply just had more land to produce badly.