A concept map is a diagram showing the relationships among concepts.
They are graphical tools for organizing and representing knowledge.
They include concepts, usually enclosed in circles or boxes of some type, and relationships between concepts indicated by a connecting line linking two concepts.
Concepts can be connected with labeled arrows, in a downward-branching hierarchical structure. The relationship between concepts can be articulated in linking phrases, e.g., "gives rise to", "results in", "is required by," or "contributes to".
The technique for visualizing these relationships among different concepts is called Concept mapping.
A concept map is a way of representing relations between ideas, images or words, in the same way that a sentence diagram represents the grammar of a sentence, a road map represents the locations of highways and towns, and a circuit diagram represents the workings of an electrical appliance. In a concept map, each word or phrase is connected to another and linked back to the original idea, word or phrase. Concept maps are a way to develop logical thinking and study skills, by revealing connections and helping students see how individual ideas form a larger whole.
Concept maps were developed to enhance meaningful learning in the sciences. A well made concept map grows within a context frame defined by an explicit "focus question," while a mind map often has only branches radiating out from a central picture. There is research evidence that knowledge is stored in the brain in the form of productions that act on declarative memory content which is also referred to as chunks or propositions.
The technique of concept mapping was developed by Joseph D. Novak and his research team at Cornell University in the 1970s as a means of representing the emerging science knowledge of students. It has subsequently been used as a tool to increase meaningful learning in the sciences and other subjects as well as to represent the expert knowledge of individuals and teams in education, government and business. Concept maps have their origin in the learning movement called constructivism. In particular, constructivists hold that learners actively construct knowledge.
Novak's work is based on the cognitive theories of David Ausubel (assimilation theory), who stressed the importance of prior knowledge in being able to learn new concepts: "The most important single factor influencing learning is what the learner already knows. Ascertain this and teach accordingly." Novak taught students as young as six years old to make concept maps to represent their response to focus questions such as "What is water?" "What causes the seasons?" In his book Learning How to Learn, Novak states that "meaningful learning involves the assimilation of new concepts and propositions into existing cognitive structures." 
Concept maps are used to stimulate the generation of ideas, and are believed to aid creativity. For example, concept mapping is sometimes used for brain-storming. Although they are often personalized and idiosyncratic, concept maps can be used to communicate complex ideas.
Formalized concept maps are used in software design, where a common usage is Unified Modeling Language diagramming amongst similar conventions and development methodologies.
Concept mapping can also be seen as a first step in ontology-building, and can also be used flexibly to represent formal argument.
Concept maps are widely used in education and business for: Note taking and summarizing gleaning key concepts, their relationships and hierarchy from documents and source materials
New knowledge creation: e.g., transforming tacit knowledge into an organizational resource, mapping team knowledge
Institutional knowledge preservation (retention), e.g, eliciting and mapping expert knowledge of employees prior to retirement
Collaborative knowledge modeling and the transfer of expert knowledge
Facilitating the creation of shared vision and shared understanding within a team or organization
Instructional design: concept maps used as Ausubelian "advance organizers" which provide an initial conceptual frame for subsequent information and learning.
Training: concept maps used as Ausubelian "advanced organizers" to represent the training context and its relationship to their jobs, to the organization's strategic objectives, to training goals.
Increasing meaningful learning:
Communicating complex ideas and arguments:
Examining the symmetry of complex ideas and arguments and associated terminology:
Detailing the entire structure of an idea, train of thought, or line of argument (with the specific goal of exposing faults, errors, or gaps in one's own reasoning) for the scrutiny of others.
Enhancing metacognition (learning to learn, and thinking about knowledge)
Improving language ability
Assessing learner understanding of learning objectives, concepts, and the relationship among those concepts