These instructions clear the FP exception flags, the exception status flag (bit 7 -- the interrupt request flag in the 8087), and the busy flag of the FPU status word. Before clearing the exception flags, FCLEX checks for unmasked FP error conditions (using an FWAIT); FNCLEX does not make this check.
FCLEX/FNCLEX can be used by an exception handler after it has processed an exception. If the exception flags are not cleared, a second interrupt request would be issued immediately.