When players talk about snowballing champions, do they mean the Champion scales a certain way or that their items they would buy would be super strong?
To clarify the confusion, there is snowball champions, and snowball items.
Snowball Champions are champions that "snowball" with kills early on. A great example of this is when you see a jungle Shaco that is running with smite and ignite. The idea behind this is that he needs to get kills early on to be useful, and if he doesn't get kills he falls behind, this is the major draw back to "snowball" champions. Most often snowball champions fall behind in late game and lose there use.
Snowball Items are items that "snowball" with kills early on, while this is kind of the same idea as snowball champions, and sometimes you will see snowball champions pick up these items. Snowball items are most commonly refereed to as items that have stacks, these often have very high risk for high reward, where you need kills to benefit, and if you die you lose a lot examples are like Mejai's Soulstealer, Leviathan, Sword of the Occult, etc. While there are other times that do stack as well (Warmogs, Bloodthirster). These items don't offer nearly as much risk as reward and cost considerably more.
Hope this helps, Cheers.
I would say it depends on the champ scales with certain Items. For Example take Singed, after he got boots and catalyst you are only able to stop him with a gank and hard CC.
It works with Udyr too just get Spirit visage and you get ultimate tankiness early ^^
You could continue this with a lot of champs and their specific builds.
Snowballing refers to when a champion who already has a good start game, has an even stronger start game. Getting a skill early and picking up another item, causes them to dominate their game, and then go and gank other lanes. To properly snowball, you have to get ahead to a point where you can push every single mistake, and then push that even harder.
Some champions are extremely good at snowballing, when other champions are not. Most of these are champions that are hard to lane with, until they get a certain line. For instance, mordekiser sucks until he picks up his revolver. Then hes hard to push out of the lane. This allows him to snowball by picking up every single cs, and pushing out his lane opponent. Other champions that you can see snowball, are champions like olaf, who gets higher damage, and more health with items. Because of his true damage leveling when he levels, he can hit for twice as much damage because the champions health should be 150 higher to take the true damage, but its not.
Leblanc is another grew snowball champion, because of her high burst. If she has items when everyone still has slightly lower health then they have at 18, she can just snowball and start bursting down people left and right.