The DSM-IV is the Diagnostic and Statistical Manual of Mental Disorders published by the American Psychiatric Association. In the United States, it is the reference used to assign diagnoses of mental illnesses.
The DSM-IV-TR is the currently used version. "TR" means it is a "text revision." This edition is being used while the American Psychiatric Association works on the next. The DSM-5 is still being compiled and will have significant changes from the DSM-IV-TR. Though the current target date is 2013, this is likely to be pushed back, because a number of serious controversies about the proposed changes exist, and in some cases - bipolar disorder included - the proposed revisions contain conflicting information.
For a description of the DSM-IV in depth, see What is the DSM-IV?.

