Snowballing is where a civ gets stronger and stronger over time until the civ becomes way more powerful than all other civs. It is based on the idea of a snowball rolling down the hill and getting bigger and bigger. It stems from how small advantages can have a cumulative effect. For example, maybe I get some extra gold from a goody hut. I use that gold to rush a settler. I use that early settler to found a good science city early on. The extra science helps me get techs before other civs. So now, I have better military units. I use those better military units to conquer my closest neighbor. Now, I have more cities than my neighbor which means more production, science and culture. So now I can build even more units and get even further ahead in science. So now, my military is even stronger. So I conquer more civs. Now, I am even more powerful. etc... Eventually, I become the #1 civ in everything, 2x more powerful than all the other civs combined.
Snowballing is tricky because on one hand, we want players to get ahead. And there is satisfaction in knowing you played well and were able to leverage your advantages to get ahead. But at the same time, once you become too far ahead then there is no challenge anymore. Winning becomes a matter of just pressing end turn. The game becomes boring. That is a bad thing. This forum has debated a lot how to best prevent snowballing from getting out of control. Some suggest game mechanics to punish the civ that is too far ahead but we generally don't like punishing players for doing well. Others suggest game mechanics to help the smaller civs catch up but those mechanics are often not enough to overcome the snowballing advantage of the civ in the lead. Still others suggest maybe just ending the game sooner when it is obvious that the snowballing civ will win.
I think civ7 tried to fix snowballing by having Age transitions. By ending an Age and resetting the tech and civics tree, it prevents a civ from continuing to get too far ahead in science or culture. So it breaks up the snowballing effect. But I have noticed that snowballing is still alive and well in civ7. This is because if you do well in the Antiquity Age and get lots of legacy bonuses, it will help you do better in the next Exploration Age. This often puts you in a good position to do well in the Exploration Age and get lots of legacy bonuses again which sets you up to do even better in the Modern Age. So there is still a cumulative effect where winning in one Age snowballs into the next Age. Also, the crisis don't really do much to hinder the powerful civ. On the contrary, the more powerful you are, the easier it is to weather the crisis. And crisis cannot be too strong that they punish the player too much because it would be frustrating to lose all your hard earned advantages from an arbitary event that you have no control over.