Team Foundation is a set of tools and technologies that enable a team to collaborate and coordinate a project (software or non software projects). The team collaboration is achieved by several tools and features available as part of "Team Foundation".
Team Foundation Server
The Team Foundation includes a server component called "Team Foundation Server" (TFS). TFS manages the central repository of the team data and enables communication between team members.
Every project team have to create a new project in TF called "Team Project". You will choose a name matching your project name. Every team member will connect to this project so that they can effectively collaborate.
Collaboration means effective communication or exchange of information between team members. Team Foundation achives this by offering several key features. The Team Project is the central repository of all data related to a project, which is shared between all members of the team. Access to data is controlled by permissions for the members and their roles.
Project Portal (Team website)
Every team project has an associated team website automatically created by Team Foundation. This website is hosted on the Team Foundation Server and is accessible for all team members. Team members can use the project portal to save/retrieve documents, view reports, exchange information by posting messages, and use other SharePoint collaborative features like calendars and lists.
Team Explorer is a plugin for Visual Studio IDE. Team members access the work items through the Team Explorer. It also provides features like checkin/checkout files, view reports and manage documents.
Alerts are (email) messages sent from TF when some events happen - like the status of a work item changes, a check-in occurs, a build is completed, or when a build status changes etc. It can be configured to send alerts to some specific members or the member who performed the specific action.
Team Foundation provides the source control functionality like VSS. You can checkin/checkout files directly from your Visual Studio using the "Team Explorer" plugin.