long-ish post up ahead lol
I tried to explain it as best as I could XD;
The story of Tiger & Bunny is set in an alternate 60's-70s timeline wherein people with superhuman powers called the "NEXT" emerged. A number of these people became superheroes, but the difference is that they are "commercialized" -- each hero is being sponsored by a company (their costumes even have their sponsors' logos/names on it. They're like walking ads/endorsers) and their heroic acts are being aired on TV (Hero TV). With every good deed they do, the heroes are able to rack up points, which, in turn, boost their rankings against other heroes. The hero who scores the biggest by the end of the season earns the title "King of Heroes".
It starts off with Kotetsu Kaburagi (also known as Wild Tiger) who is a veteran superhero. He has the power known as "Hundred Power" which amplifies his physical strength a hundred times than normal, which grants him immense strength. Though Kotetsu means good, he has an ill reputation for doing more damage than actual saving or helping people.
During a mission, a new superhero with the same ability as Kotetsu arrives. He disposes of the enemy quickly, and introduces himself to the public as Barnaby Brooks Jr. -- without even attempting to hide his real face or name, unlike the other superheroes. Kotetsu thinks of it as haughtiness on the new hero's part, which caused him to develop a dislike of him.
Kotetsu's sponsoring company then talks to him, and tells him that he'll be transferred into another company. Upon transfer, he then finds out that he's to be partnered off with another hero.... and lo and behold, it was no other than Barnaby himself. Needless to say, their partnership had a rather rocky start. Unlike Kotetsu who is brash and impulsive, Barnaby is cool and collected; a bit too calculating at times. Eventually, the two of them mend their differences and will later become a well-known superhero duo to the public.
there's actually more to it than this summary I wrote. I just can't cram it all here without spoiling anything. XD
It's a really good show, and it's one I recommend since it's not your usual superhero story :3
a lot of stuff will be revealed, like why Barnaby intentionally revealed his face, etc., and as the story progresses, the plot gets deeper and... well, better. XD
BTW if you're wondering why the title's "Tiger & Bunny", it's taken from Kotetsu's superhero name, Wild Tiger. 'Bunny' is a moniker Kotetsu gave Barnaby. LOL.