Basis

In general trading, basis is a term used to generally describe the yield spread of a broad category of bonds. For example, one might refer to the "corporate basis," to mean the spread of corporate bonds generally.

Example
The corporate basis is a couple wider today after a weak New Home Sales report. (Translation, the homes report caused corporate bonds in general to widen by a couple basis points, indicating that the home sales report was viewed as a broad economic indicator and not limited to housing sensitive companies.)

Basis can be used to describe more or less specific segments of the market. For example, in corporates, one might describe the broad corporate basis, the finance basis, or the brokerage basis. In mortgages, you might describe the mortgage basis, the 15-year basis, or the whole-loan basis.

The ubiquity of this term reveals something about the investment-grade bond market: most similar corporate bond spreads move together. For example, it would be very unusual for Bank of America bonds to move substantially different than Wachovia or Wells Fargo bonds on any given day. So if I were an owner of Bank of America bonds and saw they were trading tighter on the day, I'd first check the movement in other large banks. Most likely I'd see that other banks are moving in exactly the same manner. I'd know that the movement does not likely have anything to do with Bank of America per se, and more to do with sentiment surrounding banks in general.

In hedging, basis risk refers to the chance that the hedge doesn't move exactly with the bonds being hedged. For example, if you are hedging a portfolio of MBS with LIBOR swaps, it is possible that prepayment speeds will change such that your hedge becomes mismatched.