Welcome!
BridgeSupport files are XML files that describe the API symbols of frameworks or libraries that cannot be introspected at runtime. These are generally ANSI C symbols that is, non-object-oriented items such as constants, enumerations, structures, and functions but can also include some additional information about Objective-C classes, methods, and informal protocols.
BridgeSupport files are a major component of the RubyCocoa Objective-C bridge, and are currently examined to be used in other bridges such as PyObjC and CamelBones.
BridgeSupport is a new project from Apple. This homepage hosts the Tiger version of the project, which is less complete than the one we are working on for the upcoming Mac OS X releases, but which can still be used as a technology preview.
The releases come with pre-generated files for some of the major system frameworks, as well as a tool that you can use to cover particular frameworks or libraries. Documentation, under the form of manual pages and a DTD, is also available.
The sources are covered under a BSD license.