The phrase derives from card games where suits are considered to have different values.
Fred: Dancing isn't my strong suit. How about we go bowling instead?
From card games relying on making or ditching books or tricks, such as Hearts or Spades. In a making game, for example, if you are holding all or most of the desired cards in a given suit (hearts, spades, diamonds, clubs) then you can be fairly sure of taking a high number of 'books' or plays.
Get Melanie to talk to her for you... Diplomacy's always been her strong suit.
Interviewer: We'll let you know.