Wiktionary
n. (context architecture computing design English) A formal way of documenting a general reusable solution to a design problem in a particular field of expertise.
Wikipedia
A design pattern is the re-usable form of a solution to a design problem. The idea was introduced by the architect Christopher Alexander and has been adapted for various other disciplines, most notably computer science.
An organized collection of design patterns that relate to a particular field is called a pattern language. This language gives a common terminology for discussing the situations designers are faced with.
Documenting a pattern requires explaining why a particular situation causes problems, and how the components of the pattern relate to each other to give the solution. Christopher Alexander describes common design problems as arising from "conflicting forces" — such as the conflict between wanting a room to be sunny and wanting it not to overheat on summer afternoons. A pattern would not tell the designer how many windows to put in the room; instead, it would propose a set of values to guide the designer toward a decision that is best for their particular application. Alexander, for example, suggests that enough windows should be included to direct light all around the room. He considers this a good solution because he believes it increases the enjoyment of the room by its occupants. Other authors might come to different conclusions, if they place higher value on heating costs, or material costs. These values, used by the pattern's author to determine which solution is "best", must also be documented within the pattern.
Pattern documentation should also explain when it is applicable. Since two houses may be very different from one another, a design pattern for houses must be broad enough to apply to both of them, but not so vague that it doesn't help the designer make decisions. The range of situations in which a pattern can be used is called its context. Some examples might be "all houses", "all two-story houses", or "all places where people spend time".
For instance, in Christopher Alexander's work, bus stops and waiting rooms in a surgery center are both within the context for the pattern "A PLACE TO WAIT".