complex : a group of obviously related units of which the degree and nature of the relationship is imperfectly known — Webster See also Dictionary of Cybernetics and Systems (Principia Cybernetica), OneLook, Free Dictionary, Wiktionary, Urban Dictionary
Complexity is generally used to characterize something with many parts where those parts interact with each other in multiple ways. There is no absolute definition of what complexity means; the only consensus among researchers is that there is no agreement about the specific definition of complexity. However, a characterization of what is complex is possible. The study of these complex linkages at various scales is the main goal of complex systems theory. — Wikipedia
Complex system is composed of many components which may interact with each other. In many cases it is useful to represent such a system as a network where the nodes represent the components and the links their interactions. Examples of complex systems are Earth’s global climate, organisms, the human brain, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe.
Complex system’s behavior is intrinsically difficult to model due to the dependencies, relationships, or interactions between their parts or between a given system and its environment. Systems that are “complex” have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others. Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their own independent area of research. — Wikipedia
Emergence occurs when “the whole is greater than the sum of the parts,” meaning the whole has properties its parts do not have. These properties come about because of interactions among the parts. In mathematical shorthand, W = P + I.
Emergence plays a central role in theories of integrative levels and of complex systems. For instance, the phenomenon of life as studied in biology is an emergent property of chemistry, and psychological phenomena emerge from the neurobiological phenomena of living things. — Wikipedia
Here are links to pages about closely related subjects.