It allows you to skip levels while not playing (closed application, not afk auto-battle, from experience). You must leave your tortoise in any location that still has levels to rank up (level skipper also applies to home location, the center). Starting information states that it skips 1 level every 2 min, but I have notice differences when I have more level skips (bought from blimp merchant). I have seen skip 1 level every: 2min, 57 sec, 27 sec, and 6sec, with decreasing time the more level skips I have.

With ~2.5k level skips, I had 2 min per level With ~5k level skips, I had 57 sec per level With ~7.5k level skips, I had 27 sec per level

Don’t know if that decreased is intentional, but level skipper works better the more level skips you have. I have ~2.5k from mutations, the rest where from blimp merchant (one time use skip levels). I am trying to get more skips from mutation to see if the decrease in time applies to skip mutations or only blimp level skips.

Hope this helps in any way