The official term was coined by Jerry Laiserin, but there are as many definitions for BIM as there are people who are talking about it (but probably not using it). The definition that I prefer (and that we use at Tis the following:
BIM is an object-oriented building development tool that utilizes 5-D modeling concepts, information technology and software interoperability to design, construct and operate a building project, as well as communicate its details.
This definition considers the 3rd dimension space, the 4th dimension time and the 5th cost. Some definitions categorize BIM as 4D: the 3rd dimension is space and the 4th is the database of information that is available in the model. Other definitions (like the C3T definition) refer to the extended applications of the 3D model as "XD" since there are so many ways to utilize the model.
Personally, I like the 4D/5D method because it differentiates the uses of the 3D model, especially since most of the current applications relate to cost or time, or some combination of the two.
I consider any activity that relates to the spacial relationships in the model to be 3D: the development of the model, document coordination, the clash report, etc. The same goes for 4D and 5D; each dimension refers to a number of activities. In the future, I'm sure I will have to modify my definition to include 6D (procurement applications) and 7D (operations applications) activities. Until then, I'll leave my definition as is.