Persistently calm, whether when facing difficulties or experiencing success; not easily upset or excited.
Not easily excited or disconcerted; imperturbable; calm.
The definition of unflappable is not easily flustered.
When you can deal with an unexpected storm and the caterer not showing up on your wedding day without getting upset, this is an example of when you would be described as unflappable.
Origin of unflappable
un- +"Ž flap (“upset, stir, scandal, controversy") +"Ž -able