TR1 ("Technical Report 1") is a specification for new functionality being added to C++'s standard library. This functionality takes the form of new class and function templates for things like hash tables, reference-counting smart pointers, regular expressions, and more. TR1 itself is just a document.
The TR1 draft does not contain any background information on the functionality it provides and doesn't contain any examples for how it should be used. For this sort of information refer to the proposal documents which were used to define the TR1 functionality. The relevant proposal documents are nicely catalogued by Scott Myers.
Microsoft have recently released a Beta version of the Visual Studio 2008 Feature Pack which includes support for most of the C++ standard library extensions described in TR1.
GCC v4.x also provides support for most of the extensions.
Over the next few weeks (more likely months) I plan on playing with the new TR1 features and I will add thoughts, learnings and code snippets to this blog.