On-the-run Treasuries are the most recently auctioned securities at each standard maturity (2-year, 5-year, 10-year, etc.). They are the benchmark issues that define the yield curve and trade with the tightest bid-ask spreads and deepest liquidity.
Once a new issue is auctioned at the same maturity, the previous on-the-run becomes off-the-run. Off-the-run securities are identical in credit quality but trade at a small yield premium (the "liquidity premium") because they are less actively traded.
The on-the-run / off-the-run spread reflects pure liquidity demand:
Typical spread: 2-10 bps, depending on market conditions
In crises: the spread can widen dramatically as investors flee to the most liquid instruments
On-the-run Treasuries are important because:
Benchmark pricing: the par yield curve is fitted primarily to on-the-run issues
Repo market: on-the-run issues often trade "special" in the repo market, meaning they can be borrowed at below-market rates due to strong demand
Hedging: derivatives desks and mortgage hedgers use on-the-run Treasuries as their primary hedge instruments
Index construction: major bond indices reference on-the-run yields
The transition from on-the-run to off-the-run creates a predictable price dislocation that some relative value traders exploit.