When a bond price goes up its yield goes down. The spread on bonds is usually expressed as the difference between bonds of the same maturity but different quality, for example the difference between the yield on a 10-year Treasury vs the yield on 10-year corporate bond. Spread compression is said to have occurred when the yield on a previously higher-yielding bond comes down due to strong demand.
At the end of 2012 spread compression on emerging market debt was leading some experts to believe that demand for EM debt was overwhelming supply and leading to mispricing and the risk of exposure should US Treasury yields rise. However, the head of emerging market debt at one fund manager said he believed that more spread compression would have to take place before it could be declared a bubble.