This is a cue bid made before the partners have bid and raised a suit. It implicitly agrees the suit partner has just bid as trumps and shows a control in the suit of the cue bid.
A spade contract is unlikely to be best – East has shown six good hearts and, by not rebidding 2♠ despite having the strength to reverse, has denied four spades. Therefore, West’s 3♠ agrees hearts and shows a spade control. Depending upon the partnership style, the control may be first round (ace or void) or second round (king or singleton).
West might hold:
