A checked exception, at compile time, forces you to either declare the exception in the caller's 'throws' clause or deal with it in a 'catch' block. That is the compile-time aspect. Contrast this with unchecked exceptions which do not force you to do any or all of the above.
The run-time aspect deals with the exception itself being thrown. This can only occur during program execution. All exceptions, checked or unchecked are thrown and/or caught at run-time.
- Saish