United States Treasury securities have periodic auctions; the treasury of a given tenor, say 30 years, which has most recently been auctioned is the on-the-run security, while all older treasuries of that tenor are off-the-run.
For credit default swaps, the 5-year contract sold at the most recent IMM date is the on-the-run security; it thus has remaining maturity of between 4 years, 9 months and 5 years.
A number of indices only hold on-the-run contracts, to ease trading.
Thus, if the basis (difference in price) between an on-the-run and most recent off-the-run instrument becomes large, one may buy the off-the-run and sell the on-the-run in anticipation of the basis shrinking.
This trade, for 30-year treasuries, is notable for having been practiced by Long-Term Capital Management.