The preposition behind can be used to refer to the reasons or causes something happened or someone did something. But it can also be used to talk about the origin of something.
The preposition about is usually used to describe a connection to or association with something or concerning a topic and the information provided by talking about can describe anything and everything and not necessarily the origin or cause of something.
I hope my simple explanation does not confuse you.
It is a very normal usage, but it is not being used as a synonym of "about." It means more than that.
"The story behind" something means something that is not easy to see, something most people don't know, that explains the part that they can see.
Here are some examples.
"My name is Tonni." "That's interesting. Is there a story behind that name?" "Yes. Actually, my name is Janet, but when my brother was a baby, he couldn't say 'Janet' and called me 'Tonni,' and the name struck."
"The recurrent laryngeal nerve takes a very strange route. It doesn't take a short path. It is very circuitous. There is an evolutionary story behind that route..."
"Many people have wondered if there is an explanation of strange words of the Beatles' song, ''Lucy in the Sky with Diamonds.' During the 1960s, people suspected it had something to do with LSD. But the real story behind the song is simply that it was the title of a child's drawing. Lennon's son Julian, in nursery school, made a drawing of a classmate named Lucy, and described it as 'Lucy. In the sky, with diamonds.'"
The word "background" can be used in the same way. "Let me give you some background on why the song is titled 'Lucy in the Sky with Diamonds...'"