zen is the art of being at one with the two'ness
What's the being at one?
What's the two'ness?
Why two'ness not twoness?
I just don't know the meaning of this sentence.
There are a lot of these "Zen is the art of..." phrases, and their quality and applicability varies widely. Some are profound, and actually express truths about Zen; some are jokey and mock-profound (like this one); some are marketing catchphrases or outright parody.
The whole Zen/art meme comes from a book, Zen in the Art of Archery, published in 1948, which was among the first popular introductions of Zen to Europe and the West. As famous and popular as that book was, it was overshadowed (in the US, anyway) by the 1974 Zen and the Art of Motorcycle Maintenance (which is famously neither about Zen nor art nor motorcycle maintenance, but which I highly recommend nonetheless!) Between those two books, the connection between "Zen" and "the art of (x)" has been pretty firmly established in the collective unconscious.
"To be at one with something" means to be completely comfortable with (something) / to understand (something) so profoundly that you feel that there are no barriers between you and it. The usual usage is "at one with the Universe" / "at one with the world". (This phrase is the basis of the Dalai Lama joke that's been in the news lately.)
There's no such word as two'ness; if there were such a word it probably shouldn't have an apostrophe in the middle (so it should have been twoness.) Adding "-ness" to the end of another word is a common way of inventing a new word; like "twoness", if the meaning wasn't clear from the context, there's no point in looking in a dictionary because it won't be there.
I don't know what the context was where you saw this phrase, but I'm guessing that the writer had just been talking about duality, or the number 2, or... Tossing in a phrase like "Zen is the art of being at one with the twoness" was most likely the author trying to be funny while also emphasizing the importance of 2 (in whatever context he was talking about in the first place.)
Authors, take note: if you're trying to explain a concept, don't invent words and put them in silly mock-profound philosophical phrases and drop the whole thing into your book/article/whatever. It might make a few people laugh, but it's more likely to make a lot of people confused.
This phrase may also have been influenced by a Woody Allen line: "Students achieving Oneness will move on to Twoness."