[The following has several difficulties. I'll come back later and work on this, or at least spell out the difficulties that I see. Meanwhile I hope those with more expertise will clean it up. Nancy Glock-Grueneich)
Emergence, at its most general, is the capacity of an evolving system to develop unanticipated properties. Elements from stardust--carbon, oxygen, iron; sodium chloride; eyesight; the Internet itself. Any of the capabilities that show up only in heavier elements, compounds, later species, or eco-systems--all made up of simpler parts none of which had these properties in themselves--are "emergent".
Social systems have emergent properites as well. In economics,the results of the "invisible hand", i.e. the patterns and regularities that result from the rules and practices of the market exchange--and that are "discovered" rather than intended--are emergent properties. Arguably, much of the damage to the environment and social systems that has resulted from technological change and market driven interventions--though far from all of it--are or result from emergent properties and feedback loops of the current economic system, e.g. the rules by which investments in the stock market are made and rewarded.
Such new capabilities, for good and for ill, fit or ultimately unfit--insofar as they are properly termed "emergent"--are not intended and cannot have been predicted. In conversational approaches to conflict resolution and problem-solving, the process itself is designed and its rules agreed upon, and the general intentions of the designers at least are clear enough. But what does in fact emerge, a solution that had not been thought of, or an agreement no one had reason to expect, are emergent.
Conscious evolution may be viewed as the effort to work with evolutionary forces, i.e. those that tend to yield emergent properties, in ways that increase the likelihood that the emergent properties will be more fully functional and better adapted, enabling us as a species both to survive and to interact with other species so that all thrive.