used for building agents
(in this contexts, we mean agents in the "computer" sense of the word agents; that is a computer program
that acts on behalf of a user in some way.
BDI is short for beliefs, desires and intentions. This outlines roughly how BDI agents work. The "beliefs" in the above are some facts about the world the agent is "living" in. Based on the beliefs, certain possible courses of actions (commonly referred to as plans) become available. Once a plan is available, that becomes the agent's "desire". To achieve the desire, the plan specifies actions to be undertaken. These actions are the "intentions" of the agent.
BDI agents have been used for a number of interesting applications, from optimising use of elevator elevators, to selection of music in a shared environment, to modelling the behaviour of fighter pilots so as to create realistic opponents in combat simulations.