This sounds like a feature called Restart to Safari. I haven't actually tried it (didn't even remember it to be honest!), but I believe you can normally access it by pressing CMD +R while booting or restrict guest accounts to it. I believe it might also be coming up if the operating system is unable to boot and you need to do an internet recovery.
Since you're probably not pressing CMD + R or using a guest account, it could mean that something's gone wrong with your system. Still, it's weird that it wouldn't suggest an internet recovery but instead tosses you directly to Safari...
This probably doesn't help you a great deal, but at least you know some of the possibilities you might be dealing with.