C.D. Broad distinguished mechanistic properties, which can in principle be deduced from the properties of a system's parts and the way they are arranged, from genuinely emergent properties, which cannot be so deduced even by a hypothetical mind with complete knowledge of the parts and perfect powers of calculation, using the example, controversial even in his own day, that the liquidity of water could not have been predicted in advance from the properties of hydrogen and oxygen gas alone, but had to be discovered empirically once water itself was observed.
Applied to mind, emergentism holds that consciousness is a similarly genuine novelty, arising once neurons are organized with sufficient complexity, that is not merely a summary description of neural activity but a new kind of fact about the system as a whole, irreducible to, though fully dependent on and produced by, its physical base. This is meant to thread a needle between physicalism, which many emergentists worried left consciousness looking like nothing more than a redundant relabeling of brain activity, and dualism, which posits an entirely separate substance emergentists considered unnecessary and unparsimonious. The position's chief vulnerability is that later chemistry did, in fact, manage to explain liquidity from molecular properties after all, undermining Broad's own showcase example and leaving open the possibility that consciousness, too, will eventually turn out to be predictable in principle from sufficiently detailed neuroscience, exactly the outcome strong emergentism denies is possible.