sharing video using uiactivityViewcontroller

First get video file path

 let videoURL = NSURL(fileURLWithPath:localVideoPath)

And then pass this path to UIActivityViewController like below

let activityItems = [videoURL, "Check this out!" ]
let activityController = UIActivityViewController(activityItems: activityItems, applicationActivities: nil)

activityController.popoverPresentationController?.sourceView = self.view
activityController.popoverPresentationController?.sourceRect = self.view.frame

self.presentViewController(activityController, animated: true, completion: nil)

Updated Code for Swift 4

    let localVideoPath = "your_video_path_here..."
    let videoURL = URL(fileURLWithPath: localVideoPath)

    let activityItems: [Any] = [videoURL, "Check this out!"]
    let activityController = UIActivityViewController(activityItems: activityItems, applicationActivities: nil)

    activityController.popoverPresentationController?.sourceView = view
    activityController.popoverPresentationController?.sourceRect = view.frame

    self.present(activityController, animated: true, completion: nil)

To share video from Local Document directory path

func shareVideo(videoPath : String){
        let localVideoPath = videoPath
        let videoURL = URL(fileURLWithPath: localVideoPath)

        let activityItems: [AnyObject] = [videoURL as AnyObject]
        let activityController = UIActivityViewController(activityItems: activityItems, applicationActivities: nil)

        activityController.popoverPresentationController?.sourceView = view
        activityController.popoverPresentationController?.sourceRect = view.frame

        self.present(activityController, animated: true, completion: nil)
    }