Treasury securities that are older in issue, thus have the less liquidity than the on-the-run counterpart. The reduced liquidity means it is off-the-run. These securities will trade at a discount compared to the newer issues.
Since US Treasuries are used as collateral for short-term lending, the liquidity means the on-the-run securities trade at a premium. While Treasuries are high quality collateral in general, T-Bills are considered pristine. They tend to always be on-the-run as compared to notes and bonds.
With collateralization, lenders are always concerned with liquidity in case of a default. For this reason, they offer the best deals for on-the-run assets. Off-the-run securities can still be widely desired, just not as in demand as the newer ones.