Hello abdelmajidfromwashington,
Thanks for posting on Apple Support Communities. From what I gather you are trying to restore your iPhone via your Mac. The necessary software for the restore started downloading and then a few minutes later your phone restarted. Did the download complete on the computer before your phone restarted? You may need to restart your computer, put your phone in recovery mode again, and start the restore over. Follow the steps outlined in this article:
If you can't update or restore your iPhone, iPad, or iPod touch
Have a great day!