In ordinary English, emergence means the reappearance of something that was hidden before. In the philosophy of science emergence is also used for the appearance in a whole of something that was not there in the parts. Searle, for example, uses "strong emergence" for the appearance of consciousness out of matter. To buttress his case, Searle gives two other examples of "strong emergence": fluidity and higher order patterns in the game of life, but neither is convincing. The laws of fluid mechanics can be derived mathematically from the properties of the molecules making up the fluids concerned. In fact, amongst physicists fluidity is a standard example in support of physicalist reductionism, to which Searle is opposed. In the game of life, the higher order phenomena (like lines and triangles) do not actually appear within the world of the game itself, because the entities that make up the game have no way to detect them. They occur only in the minds of the human observers who recognise them because they have these patterns already as pre-existent structures within their own human mind. In short: both examples prove the opposite of what Searle thinks and the simple fact remains that consciousness can only emerge out of the material brain if that brain already housed consciousness in some form or another beforehand.
It is hard to believe that anyone takes "strong emergence" serious because it can be used to "explain" absolutely anything. How far would science have come if it had accepted that mice "emerge" out of old rags, or that the sun "emerges" above the eastern horizon in the morning?