I'm not sure but webkit is a type of internet browser. Could be safari or firefox or some other browser that's open on your computer. My guess is you're running some version of OS X since you have the "com.apple.webkit" prefix listed in your question. I would gather that Safari is open and needs to be Quit completely for the installation to proceed. However you do not have to quit your web browser with Flash 18 and above.
Currently Flash Player requires all applications that may be using it to be closed before installation begins. If it can't identify the exact name of the app, it'll show the process name, which is what you're seeing. You can try to use the Activity Monitor (viewing all processes from all users) to identify the process and if so, kill it via the Activity Monitor.
We are changing this behaviour in an upcoming release of Flash Player, where the installation process will not require the closing of apps that are using it and instead leave it up to the user to close the app at a convenient time and relaunch to load the newly installed Player. This functionality is currently available in the latest beta version posted at Download Adobe Flash Player 18 Beta for Desktops - Adobe Labs. If you decide to install the beta do keep in mind that performance/functionality may be unstable. To revert to the release version, simply uninstall the beta (uninstaller is also posted on the same page) and then go to get.adobe.com/flashplayer to download the release version.