Bond spread (or credit spread) refers to the difference in the yield of two bonds because of the difference in their credit ratings.
The credit rating of a bond reflects the risk profile of the bond. For example, BB-rated corporate bond will be riskier compared to a Treasury security issued by the Government, which is considered risk free.
In this case the bond spread for this BB-rated security will be the difference between the yield of the security and that of the Treasury security.
The bond spread reflects how much extra the bond buyer is being compensated for taking the extra credit risk.