Unlike other super sentai shows, Akibarangers takes place in a world that is modeled after ours, in the sense that there are no superheroes nor villains and all the other super sentais are just popular TV shows by Toei Corp. In fact, one could even think that it's set in the real world, if not for a surprising twist later on in the series (more on this later). The show follows a 30-year-old anime and super sentai geek named Nobuo Akagi, a 27-year old perverted female cosplayer named Yumeria Moegi, and an aspiring martial artist named Mitsuki Aoyagi.
Akagi, Yumeria, and Mitsuki were all recruited by a mysterious and beautiful maid cafe owner named Hakase Hiroyo and asked to become members of the Unofficial Sentai Akibarangers, so that they can protect the Akihabara district from powerful villains, with the catch being that everything - from their transformation to their fights with the villains - only happens inside their heads. They use a weird anime toy called the Moe Moe Z-Cune in order to transform, while Hakase monitors their progress through a computer.
It should be obvious from the synopsis that Akibarangers is not meant to be taken seriously. It's a self-admitted comedy series that makes fun of the whole super sentai subculture via trope subversions and frequent breaking of the fourth wall. However, the twist is that there's a much deeper, and more serious story hidden underneath Akibarangers' satirical take on the otaku culture. I mentioned above that it could almost be set in the real world, except for one crucial twist: over time, the enemies they fight inside their heads managed to break through the walls of their imaginary world. Causing all the fighting to spill out into the one place where the Rangers have no power: the real world.
I won't reveal the other major twist to the story, as that would ruin the whole thing. Let's just say that the Akibarangers have a much bigger and more powerful enemy to fight than the ones who escaped from their delusions.
The show's first season consists of 13 x 24 minute episodes, and they can be enjoyed as simple comedies or as one mini series that has small moments of drama and action. The only downside is that you need to be familiar with the super sentai genre, other wise you'd miss out on a lot of in-jokes and references.
If you want to check out the show, NAMCO Bandai has made the first season available via their youtube channel (you'd have to search for it yourself, as they have disabled embedding). The episodes have English subtitles, but I have heard that it is not available for some countries. There's also an unofficial translation floating around on the Internet (or on Vimeo), but the legality of said copies is up in the air.