Stein can be an exceptionally difficult writer to understand as she was trying to break writing conventions and force people to concentrate on her words. She relies heavily on repetition and sometimes on punning to make her points.
If we put this quote into a fuller context, we can start to understand it:
I am writing for myself and strangers. This is the only way that I can do it. Everybody is a real one to me, everybody is like some one else too to me. No one of them that I know can want to know it and so I write for myself and strangers.
As a little bit of background, Stein tends to write about Americans as strange or foreign. For instance, the title of her book Four in America, that covers such iconic American figures as the Wright brothers, is a pun on "Foreign America." So for this ex-patriot lesbian, typical American life and values are strange or alien. Her is a different, more elite viewpoint.
Thus, when she says she is writing to strangers, that first includes most of her audience. But more specifically, the people she is writing about are also strangers because they won't recognize themselves in the book. "Everyone is a real one to me," she says, meaning she is writing about real people. "But everyone is like someone else too to me," she says, saying that each of these real individuals is a type too. All of this will be "strange" to the people she is writing about because "no one of them ... can want to know it." People, she says, don't like to accept that they are types as much as individuals.
In the end, she says, people won't understand what she means, so they will remain strangers and not intimates. She repeats this over and over. She says she wants readers, so she has to accept strangers. But since she will understand what she means, she writes to two audiences: herself--who understands--and strangers--most of the rest of the world, which refuses or is unable to see what she sees.
Stepping into Stein's writing is stepping into a truly other world, one that reflects ways of thinking we have to some extent abandoned. One of these is her notion that the artist understands and sees things that the rest of the mere mortals of the world don't.