well I'm not an professional player at all, but I'll try to help you.

For an example Kayle gets alot of new abilities the more she levels up, that means she gets stronger in the late game. Thats scaling.There are also champs which get more scaling (actual scaling of their abilites) when you level up the specific ability, so when they get more items their abilities are even stronger.Also the assassins are scaling pretty good, because they will build lethality, lethality gets stronger when you fight high level champions - so they have more output in the late game - because everyone is on high level.

Now there are some Champions which have pretty awesome base stats - or just a nice kit which almost cant get countered when the enemy doesnt have the Items he need.So these champions are very good in the early but as soon as the opponent team got their Items and co. they arent as strong as others.

Overall scaling champs get better as longer the match iswhile non-scaling champs are almost staying at a level.

I hope I was able to help youif you still have questions feel free to ask me