What's the easy button do when you are reviewing the kanji? I can't find anywhere on the site that mentions it.
It goes to the next box, but it's scheduled 1.5 times further away than the box normally would be. So Box 2 would be ~10 days while box 4 would be ~45 days.
Basically, if you get a kanji that you know really well, and can write it the second you see the keyword and remember the full mnemonic story, then hit the easy button. It'll push it further along the review cycle than just saying "yes" will.
It's really kind of up to you how you use it. Most people studying Japanese would use it on the first 200 or so super-easy beginner kanji such as numbers and common verbs like 見る、食べる. It doesn't ever bother me to see kanji like that again. It's a nice confidence booster.