Definition.com
Emergence is a co-operation of things of unlike kinds, not an adding measurable motion to measurable motion, or things of one kind to other individuals of their kind.
Definition.com
Emergence is a process whereby the emergent is unlike its components. It's components are incommensurable, and cannot be reduced to their sum or their difference.
Definition.com
Emergence is epistemologically, the idea that complex systems are too complex to be explained by reductionistic practices. Ontologically it is the idea that new entities with their own properties and causal powers arise and are part of the furniture of the universe.