I have now installed and used TFS at a number of clients.  On every installation the very first question asked has alway been, what is a project?  This question seems to provoke a solid hour of conversation about organization structure and development practices.  No doubt every shop will always be different, regardless you will still derive from some base.  Last night while browsing around on MSDN, I ran across the official "project" party line.  Below is just a snippet from Team Foundation Team Projects.

The Logical Definition of a Team Project

Logically (or conceptually), a team project is a single infrastructure that encompasses all of the separate tools and elements used in the life cycle of the development of a software application. Each software application, or "team project," in development is virtually grouped in its own namespace intended solely for the team project. Therefore, a team project is simply a container isolating all of the tools and artifacts associated with a particular software application in development, such that all other team projects will not have access to those tools or artifacts (for example, source code, work items, and documents).

The team project is the central concept that holds together the team endeavor of creating a specific software technology or product. The team project is the virtual collection of artifacts relevant to a software application on which a team is working. For the team members, the team project concept eliminates the problem of having access to multiple artifacts not relevant to the team project; such an excess of artifacts causes confusion and delays the software development process. At a minimum, the team project consists of a set of tools and artifacts. The team project may also include source control policies, a team project reporting site, and a team project portal. The Team Foundation team project allows the process template, during the creation of a team project, to select which tools are relevant and will be added in the team project container.

The team project concept enhances reporting across all the tools used by the team. In the past, cross-tool reporting was challenging because the data from different tools was not related. For example, if a software developer wanted to obtain a cross-tool report on defects, he or she would have to distinguish the defects from multiple projects, since the defects were all stored in a common location. A team project is created in a namespace containing only tools and artifacts relevant to the software project; therefore a common filter is created which can relate different artifacts from different tools.

A single Team Foundation Server server may contain multiple team projects, each of which are created in a separate namespace, such that a document named X in namespace A is not the same as a document named X in namespace B. Creating a team project in a separate namespace allow artifacts or tools to be unique to the team project for which they belong, such that a tool or artifact contained in team project A is not accessible to a software developer working on team project B.

MSDN | Team Foundation Team Projects, http://msdn2.microsoft.com/en-us/library/ms181234(VS.80).aspx