Compatability testing means testing the application build 
on different platforms whether the application build is 
able to run on different platforms or not.

platforms means O/S,Browsers,Compilers,Other system 
software.

There are 2 types of Compatibility testing...

Forward Compatability
Backward Compatability.

suppose executing a build on unix o/s which is developed in 
Microsoft Languages like VB.Forward compatability

executing the lower versions of s/w on higher versions of 
platforms......Backward compatability.

enjoy......