When I first started reading about things like psychedelic drugs back in high school, I remember certain writers would talk about experiencing "ego death" while tripping.
"Ego Death." That seemed very strange to me - I couldn't wrap my mind around the concept. How could one lose one's very self? And the term "death" seemed so final, so black and white.
The first time I really saw it clearly was on a high dose of mushrooms. "I" was gone in a sense, the experience was more like a field of awareness in which everything was happening. It was as if I was on a ride, and I was the last one to become aware of what was actually happening. Ah, the body is getting up - what is it doing? Oh, it's headed to the kitchen, looks like it's getting something to drink. It was all happening without a conscious plan, self forgotten. Universe-hand meets universe-lemonade.
From that perspective (trust me), the idea of labeling things as separate can be seen as a bit of an assumption, albeit a very useful one. Sometimes people refer to "oneness" or a sense of interconnectedness. Oneness is a bit too simple. It's really more of a mystery, an unknown - the danger here is that oneness becomes a sought after concept just like the labeling of dualism, of separateness. So in Hinduism they call it Advaita which means "not two". Not two is also a bit clumsy, but it kind of sidesteps the over-simplicity and labeling problem with the term oneness.
This also points to the Buddhist concept of no-self, anatta, and the Advaita area is similar to certain parts of Buddhism such as Dzogchen or Mahamudra.
What you are identifying with is just a body which was indoctrinated by language (subject-object) and culture to believe in a self, a self-identity, much in the same way people believe in god or politics or gender roles or what have you. But it's just a body, a piece of meat, that just happens to be doing what it is doing.
Science would tell you that you are not separate, the impermanent collection of molecules that temporarily compose your body cannot be removed from the universe. And you are constantly changing, exchanging gases, fluids and solids with what you perceive to be not you.
Science would also tell you that you have never experienced anything other than your own mind, so theoretically it should be possible to experience it as one, one mind. Everything you have ever experienced is more like a map of the universe that you have created, and hopefully that map is relatively accurate in the right places. But it's all kind of made up. Colors do not exist, those are your map to electro-magnetic frequency information.
Anyway, hopefully I've thoroughly blown your mind by now.
I wanted to share a few pointers to the non-dual / Advaita stuff I've come across over the years. These teachers point directly to this experience, and some people seem to be able to pick it up this way. I found I had to deal a number of body blows to the ego with daily meditation and a number of experiences with psychedelics to fully grok it. Meditation, taken far enough (stream entry, say) can be very effective in this regard.
The Advaita tradition goes back a ways, but Ramana Maharshi is probably the most popular of the earlier teachers. Ramana's lineage includes Papaji and Gangaji.
Probably the most popular modern teacher would be Eckhart Tolle, thanks to Oprah Winfrey's interest. I tend to prefer Adyashanti as he has the rather amazing gift of being able to talk about the same thing over and over again without really repeating himself, and he has an extensive background in Zen. Although not so much about Advaita, Adyashanti's book, The End Of Your World should be required reading for people who have woken up a bit.
I Am That, is very good but is slightly more inscrutable than some of the more modern works mentioned below. Nisargadatta's lineage includes Aussie Sailor Bob Adamson (very direct, simple pointing) who I became familiar with by way of The Advaita Podcast, created by fans of Bob.
Nothing Personal, is probably my favorite general book for this category. I would consider this more readable and direct than the classic Ramana and Nisargadatta. The first few pages are classic direct pointing.
Two Russian women, Ilona and Elena, have created a book which details their very fresh, brash, direct approach to realizing no-self. Gateless Gatecrashers consists of a number of dialogues with people seeking this understanding. For some this is perhaps a bit too direct, but this is quite an addition to the nondual approach, and they have an extensive website and forums for support.
Finally, in part, the catalyst that kind of got me to write this post was coming across the film, Living Nonduality, that features interviews with non-dualist Robert Wolfe and some of his followers. They get it.