Passing functions as parameters in Swift

Oneword answer for your question is Closures

The Default Syntax for closures is () -> ()

Instead of Selector you could directly mention the method definition

func showConfirmBox(msg:String, title:String,
    firstBtnStr:String, firstSelector:(sampleParameter: String) -> returntype,
    secondBtnStr:String, secondSelector:() -> returntype,
    caller:UIViewController) {
    //Your Code
}

But using this will create readability problems so i suggest you to use typeAlias

typealias MethodHandler1 = (sampleParameter : String)  -> Void
typealias MethodHandler2 = ()  -> Void

func showConfirmBox(msg:String, title:String,
                    firstBtnStr:String, firstSelector:MethodHandler1,
                    secondBtnStr:String, secondSelector:MethodHandler2) {

    // After any asynchronous call
    // Call any of your closures based on your logic like this
    firstSelector("FirstButtonString")
    secondSelector()
}

You can call your method like this

func anyMethod() {
   //Some other logic 

   showConfirmBox(msg: "msg", title: "title", firstBtnStr: "btnString", 
         firstSelector: { (firstSelectorString) in
              print(firstSelectorString) //this prints FirstButtonString
         }, 
         secondBtnStr: "btnstring") { 
           //Invocation comes here after secondSelector is called

         }
}