Let me start by saying that the factors for the emergence of the Russian Empire are quite complex and still not fully understood. Most important were probably geography and geopolitics. Essentially, the steppe or prairie between the Southern-European Part of Russia towards Asia was a gateway for Asian nomads to enter Europe. Amongst these nomadic peoples, the Mongols were just one of the dangers Russia had to face from the 13th century onwards. The steppe posed a great danger and challenge to Russian survival for a long time - as a border and periphery. It was an important factor for the militarisation of Russian society (and also for its autocratic character.)

The Mongols ruled over large parts of Russia (at that time the Kievan Rus) for about 200 years until the Muscovite princes managed to gain more and more power and eventually pushed them back. During this struggle, Moscovite Russia became a strong, disciplined autocracy.

After the end of Mongolian dominance, Russia resumed its struggle for secure borders. Not necessarily to gain territory, but to secure and defend its borders, Russia had to expand into the steppe against its enemies. The nomadic peoples were pushed back to the natural borders of the Caucasus, the Carpathian Mountains, Pamir, Tien Shan and the Altai Mountains.

During the middle of the 16th century, Russian expansion exceeded the territory of its predecessor, the Kievan Rus. Moscovite Russia under Ivan I. fought successful military campaings against the powerful Tatars and conquered their strongholds in the East and Southeast. After this, the path to Siberia and other formerly Mongol regions was clear.

Russian traders and merchants, supported by Moscovite troops, began the great expansion to the East. This expansion was facilitated by the generally unsecured and loose state of Russias western borders. It was also caused by the attempts of the western neighbours to spread Catholicism in Russia and by Moscow's aim to regain the Kievan lands under Lithuanian and Polish rule. Furthermore, Russia sought to gain access to the Baltic Sea and Black Sea to end its status of being surrounded by land only.

The Muscovite state was able to expand into Asia rather quickly due to a lack of strong barriers and a successful system of communication along the waterways. Russia was able to thus expand without having to control the open sea.

During the 18th century, Russia entered a new imperial age and expanded in multiple directions, militarily and peacefully. Siberia was fully conquered and Russia advanced all the way to the Far East. The expansion to the East can be compared to the American conquest of the western regions, although it was more peaceful and less bloody than the latter.

When Russia's expansion ended it's "natural" borders were reached, it was an empire and well protected from outside attacks. From then on, the vast territory and harsh climate helped repel most invaders.

To summarise, Russia mostly comquered areas and peoples it already knew quite well. The Russians colonised lands in close proximity to its borders one after the other - areas inhabited by ethnicities that mixed with Russians for centuries. On numerous occasions, Russian expansion happened with consent or even after requests by the then colonised people. These were certainly some of the reasons for the success of Russian imperialism during this time. Russians did not view themselves as superior and only later did they attempt to "russify" other ethnicities, which certainly partially led to its downfall.

Alright, this was my attempt at a little summary of what I learned about this at university. I have some texts I could recommend in case you want to read more :) Hope this was helpful!