On-the-run Treasuries are the most recently issued U.S. Treasury bonds or notes of a particular maturity. "On-the-run" Treasuries are the opposite of "off-the-run" Treasuries, which refer to Treasury securities that have been issued before the most recent issue and are still outstanding. Media mentions about Treasury yields and prices generally reference "on-the-run" Treasuries.
Off-the-run treasuries are all Treasury bonds and notes issued before the most recently issued bond or note of a particular maturity. These are the opposite of "on-the-run treasuries."