What does Snowballing mean?
Solution 1:
Snowball is the term used when a team or character just gets better and better (usually from getting fed) to the point where it is very difficult to stop them. Much like a snowball rolling down a hill getting bigger and bigger.
An easy example of a snowball is an early game team fight. The team that comes out on top has a gold/xp advantage for the next team fight, making them stronger. They win the next team fight because of it, gaining a further advantage of gold/xp.
Solution 2:
Like a snowball rolling down a snowy hill that grows bigger and bigger as it goes down (you know, cartoon like), it become hard to stop as it gets bigger.
Many champions can have the same effect on a game in League : They get gold and levels advantage over the enemy champions that they are extremely hard to stop.
That happens when one can get many kills without dying early in a game.
With the gold, they get better items than the enemy and with the levels, their skills deal more damage, they have more base health, base resists, etc. The 2 combined make that champion "snowball" as these advantages will only get bigger unless stopped.
Solution 3:
Snowballing is the term used for the effect of one team or player becoming stronger and stronger and thus winning fights easier and easier because the team or player won a few fights before.
Note that the most determining factor for whether a team (or champion) can snowball is whether their champion stats scale well with better items/levels or their skills scale well with better items/levels. In other words, how much their potential increases from simply having a bit more gold or a few more skills/levels.
This is why it's often said that specific champs are snowball champs. Because they have skills and or stats that scale or do things so well, that the sheer act of leveling up or winning one fight already gives them a massive advantage