Wikipedia
The many-to-many communication paradigm is one of three major Internet computing paradigms, characterized by multiple users contributing and receiving information, with the information elements often interlinked across different websites. Developments such as file sharing, blogs, Wikis, and tagging are media forms that reflect this paradigm; these contrast with both the one-to-one (characterized by e-mail, FTP, and Telnet) and one-to-many (characterized by websites) paradigms.
With the evolution to the full "many-to-many" computing paradigm, people can input and receive information to and from the Internet; they will be able to connect and communicate dynamically within a flexibly formed scope; there will be no artificial boundary between information and communication tools, and the definition of "many" will go well beyond people to include entities such as organizations, products, processes, events, and concepts.
In systems analysis, a many-to-many relationship is a type of cardinality that refers to the relationship between two entities A and B in which A may contain a parent instance for which there are many children in B and vice versa.
For example, think of A as Authors, and B as Books. An Author can write several Books, and a Book can be written by several Authors.
In a relational database management system, such relationships are usually implemented by means of an associative table (also known as cross-reference table), say, AB with two one-to-many relationships A -> AB and B -> AB. In this case the logical primary key for AB is formed from the two foreign keys (i.e. copies of the primary keys of A and B).
In web application frameworks such as CakePHP and Ruby on Rails, a many-to-many relationship between database tables in a model is sometimes referred to as a HasAndBelongsToMany (HABTM) relationship.