Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
Getting Error When Trying To Download iOS 7
As expected Apple officially released iOS 7 for iPhone, iPad and iPod touch and as expected the servers are currently getting hit by thousands of people trying to download the same files meaning that many users are bumping in to errors.
The best thing to do for now and the only solution is to wait a couple of minutes and try again because refreshing every second just adds to the problem.
If you don’t know how to install iOS 7 we have a full guide available here