It is an expression used in sports like baseball, golf or boxing that means you have failed and missed the hit, so you get no points. In everyday life this expression is used when you miss the aim or the target of an action: for example when telling a joke that was supposed to be funny but it is not, flirting with a girl who pays no attention to you in the end… and so on. It is sometimes tranlated into Spanish like “tocado y hundido” (as in our battleship game- which in English is “hit and sunk”).
1: I told her my feelings about her.
2: Ah… Did it go down well?
1: Nope, swing and a miss.