The anime talks about the characters leveling up, as if they somehow know that they aren't real. If you or I gained more skilled, we'd say we became more advanced in X skill, or were more skillful that we were previously. Or is this something that is in the manga's backstory that isn't fully explained in the anime?
Well in the dub for anime some one has to come up with the words for the script to the best of their ability.So it's just their choice in words.
More than likely it's a slightly inaccurate translation of a word or phrase that means to "improve" or "become more skillful".
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