To become ridiculously more attractive than one's former self, primarily, but not exclusively, as a result of puberty. A pun on 'level up', referencing the unexpected transformation of Neville Longbottom (Matthew Lewis).
"Did you see what that kid from ET looks like now?"
To get significantly more attractive after going through the process of puberty.
Origin stems from Harry Potter, where the character Neville Longbottom (actor: Matthew Lewis) went from a dumpling shaped (but very sweet) 11 year-old to a daaaamn fine (and still very sweet) 25 year-old today.
The word was popularised by tumblr usage as both a noun and a verb.
Me looking in the mirror: I'd better Neville Longbottom by the time I get to uni, or I'm going to die alone. :/
Person returning home from uni: Is that...? Is that Susan?! Well she certainly Neville Longbottomed.
Person referring to their boyfriend: Nah, I'm not gonna break up with him. Yeah he's kinda pudgy, bit fingers crossed he'll do a Neville Longbottom!