I think it is a re-statement of the understanding of non-duality, which really means 'not divided' or 'not two'. 'Advaya' is the Buddhist term for non-dual (as distinct from advaita).
Non-dual is not the same as 'one' as it doesn't refer to a singular or numerical one. It is, if you like, a unity which is not an entity. It is more that all sentience originates from the same source, or is cut from the same cloth, so to speak.
Here's something I wrote on Philosophy Forum about it:
I think the idealist or perennialist understanding of the fundamental unity of being ought to be understood in terms of a unity which is not an entity. What I mean by that is that the underlying unity of the Cosmos ought not to be conceived of as numerically singular, that is, as one of something, but as being the underlying unity from which diversity emanates.
But the notion of 'the one' as being numerically single, that is, an instance of something, straight away implies another, namely, someone who is aware of that one, or at least the possibility of something or someone else who is distinct from 'that one'. In other words, if you have a numerical '1', then by implication you already have other numbers from which '1' is distinguished, as the concept of '1' is only meaningful in relation to other numbers.
Whereas, the One in the classical sense, is beyond enumeration and any sense of discrete identity (i.e. being 'this one' as distinct from 'that one'.) So 'the One' is a unity which is not an entity. It is more like: the One that the Many arise from, but from which they are never really apart, because to the extent that they are beings, they embody and reflect the One which gives rise to them (which, I think, is a Neoplatonist way of understanding it.)
But I don't think it's very Buddhist. It's much more characteristic of syncretistic philosophies, like the Evans-Wentz translation of The Tibetan Book of the Great Liberation, which drew in ideas from many sources. (A new translation of that same text, Self-Liberation through Seeing with Naked Awareness
, John Myrdhin Reynolds, has comments on Evans Wentz's translation, but there's nothing at all in it about the 'one mind' that Evans-Wentz waxed eloquent about.)
The other point is that mysticism is a recognisable trait in many different traditions. Mystics all tend to have some things in common, no matter what the background. And mysticism is really hard for the non-mystic to understand - hence the use of the word in a derogatory sense, as a kind of catch-all term for 'woolly-headedness'. But it has own inner logic and consistency for those with ears to hear.