You are returning test: Dictionary<String,AnyObject>from a closure method, not from homePageDetails. The return return type Voidis why you get this error.
Alamofire, Alamofire.request . , . - . :
func homePageDetails(userName:String, completion:(Dictionary<String,AnyObject>) -> Void) {
let username = userName
let hompePageDetails = Alamofire.request(.GET, "http://example.com/API/Bunch/GetHomePageDetails/\(username)/").responseJSON{(request, response, JSON, error) in
print(JSON)
var test = JSON as Dictionary<String,AnyObject>
completion(test)
}
}