The anxiety about form and formal causation (Aristotelian term!) in modern science and philosophy is probably what gives rise to the mystery and slight fascination or dread surrounding notions of emergence. Somehow we want causation to be clunky, to involve materialities bonking into one another like the proverbial metal balls in the proverbial executive toy.
But if causality happens because of shape (as well as, or even instead of, because of matter) then we are forced to consider all kinds of things that materialist science, since its inception, has had trouble with (such as epigenesis). Formal causes are precisely the black sheep of science, marked with a big scarlet letter (S for Scholastic).
Emergence steps in as a kind of magic grease to oil the engine presumed to lurk in the sub-basement of reality beneath objects.
For my OOO, however, emergence is always emergence-for or emergence-as (which kind of means the same thing). Think of a kettle boiling. What is happening? Electrons are quantum jumping from lower to higher orbits. This behavior, a phase transition, emerges as boiling for an observer like me, waiting for my afternoon tea.
The smooth, holistic slide of water from cool to boiling happens to me, an observer. Just like the way the dalmatian pops out of the patches of black and white (see my previous). Emergence appears unified and smooth, but this holistic event is always for-another-entity. It would be wrong to say that the water has virtual properties of boiling that somehow “come out” at the right point. It's less mysterious to say that when the heating element on my stove interacts with the water, it boils. Its emergence-as-boiling is a sensual object, produced in an interaction between kettle and stove.
Likewise, on this view, mind is not to be found “in” neurons, but in sensual interactions between neurons and other objects. There is some truth, then, in the esoteric Buddhist idea that mind is not to be found “in” your body—nor is to be found “outside” it, nor “somewhere in between,” as the saying goes.
There is far less mystery in this view, but perhaps there is a lot of magic. The ordinary world in which kettles boil and minds think about tea is an entangled mesh where it becomes impossible to say where one (sensual) object starts and another (sensual) object stops.