I don't know when chuunibyou became such a big deal in anime, but it seems to have exploded from nowhere. All of a sudden, every high-school anime seems to have a character with delusions of grandeur based around their (maybe genuine?) belief that they have supernatural powers or a long line of historically-significant past lives. The term is apparently a genuine "middle-school second-year syndrome" where young teenagers act out elaborate fantasies to varying degress in an attempt to... I'm not sure.
The most visible example of this in anime is Chuunibyou demo Koi ga Shitai! - an insipid moe show about a guy indulging a younger student's delusions until she falls in love with him - but these characters seem to be popping up all over the place these days.
In most anime cases, the afflicted character doesn't actually have supernatural abilities; they just pretend or imagine that they do. What makes Charlotte a bit different is that not only do its characters actually have powers, it explains why the chuunibyou phenomenon is so short-lived.
Similar to mutant powers in X-Men, abilities in Charlotte emerge during adolescence, but disappear by adulthood. So the various characters' superpowers - which range from mind control to telekinesis - will only be usable for a few years.
The other great thing about Charlotte's superpowers is that each one has a ridiculous limitation that makes it practically worthless.
Otosaka can take control of someone else's body - but only for five seconds at a time, and his own body is catatonic (usually having faceplanted in the street) for the duration. Takajou can "teleport" - but in practice just moves imperceptibility fast in a straight line until he's stopped by an impact. Tomori can turn invisible - but only from one person at a time, remaining in plain sight to everyone else.
The three of them make up the core of the student council at their school, which is specially set up to find and gather children with powers, protecting them from discovery and experimentation until they're old enough for their powers to disappear.
For the first six weeks the show has been pretty lighthearted, focusing on the ways powers can backfire or be misused for comedic effect (and profit). It's had some serious moments - Tomori's back story and her behaviour when revealing it to the protagonist are at odds with her usually-carefree personality, which is jarring - but the final moments of the most recent episode have taken a turn towards a darker tone that will hopefully drive the story with a bit more force.