Emergence is...

1) ...what parts of a system do together that they would not do by themselves: collective behavior.
2) ...what a system does by virtue of its relationship to its environment that it would not do by itself: e.g. its function.
3) ...the act or process of becoming an emergent system.
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According to this view, when we think about emergence we are, in our mind's eye, moving between different vantage points. We see the trees and the forest at the same time. We see the way the trees and the forest are related to each other. To see in both these views we have to be able to see details, but also ignore details. The trick is to know which of the many details we see in the trees are important to know when we see the forest.

In conventional views the observer considers either the trees or the forest. Those who consider the trees consider the details to be essential and do not see the patterns that arise when considering trees in the context of the forest. Those who consider the forest do not see the details. When one can shift back and forth between seeing the trees and the forest one also sees which aspects of the trees are relevant to the description of the forest. Understanding this relationship in general is the study of emergence.

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One of the problems in thinking about the concepts of complex systems is that we often assign properties to a system that are actually properties of a relationship between the system and its environment. Why do we do this? Because it makes thinking about what is going on simpler. Why can we do this? Because when the environment does not change, then we only need to describe the system and not the environment in order to give the relationship. Thus, the relationship is often implicit in what we think and what we say.
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Concepts in Complex Systems
Yaneer Bar-Yam

Slots and Values
object	Sante Fe