The purpose of this site is to explore designing for context. Oxford dictionary defines context as "the circumstances that form the setting for an event, statement, or idea, and in terms of which it can be fully understood and assessed." Contextual Design aims to design systems that can understand and assess these circumstances. Doing so and comparing them to a user's preferences, can allow this system to predict and then preempt the user's actions. The more information a system has, the better it can understand what is happening at any given time – and what it should do. If a system does this well enough, it can be fully autonomous and not even require any explicit input from it’s user.
It is worth noting how this definition of Contextual design differs from an existing definition of as coined by Beyer and Holtzblatt. They describe Contextual design as a design process which "...incorporates ethnographic methods for gathering data relevant to the product via field studies, rationalizing workflows, and designing human-computer interfaces. In practice, this means that researchers aggregate data from customers in the field where people are living and applying these findings into a final product." (Wikipedia) The tools Beyer and Holtzblatt lay out are indispensable in User Experience design; they are evaluative tools that allow us to identify opportunities and solutions. But they are referring to designing in context rather than for context. These definitions are not conflicting in any way - just different uses of the same term.