If you Save your Screener , below are the advantages :

Save Time : You do not have to choose all the filters again. You can go to My Screener and directly run/execute your screener.

No Need to be in front of the Terminal : While saving your screener , you can subscribe to it. If you do that you will be automatically alerted on your SMS and email if any trade alerts are generated by the screener. So you do not miss any alerts if you are not in from of the system.

Flexible Configuration : You can configure the system in such a way that you can tell the system at what frequency you want to receive the SMS , whether you want to receive for all the scrips or only the scrips saved in your Watchlist(which you may be interested in).