The blue screen of death is a term I've come across occasionally over the years, and I'm assuming it's that awful screen that suddenly reverts to giving you information in what looks like a typeface from the 1970s on your screen, and that starts to do things you're not entirely clear about. Or just sits there looking at you with a kind of huh!-you-don't-know-what-to-do-now look on its face.
I was reminded of the phrase when reading a review of the latest update of Avira's free antivirus system (which I'd come across via a reference to the Avira Endpoint Security page). In the review the writer talks about how Avira's newest antivirus is aggressive enough to uninstall any other antivirus system you may have installed, but their concern was that on some systems this would result in the BSOD. It's rather like bringing a alligator into your house when you've had a chihuahua. The alligator eats the chihuahua alive, in one gulp, and that may cause a bit of an after-mess on the floor (from one end or the other). The BSOD is the equivalent of such a mess.
That apart, the Avira seems like a pretty good system. However antivirus systems have a way of taking over and it's worth checking such a system out with a friend before you go further. Alligators are great for demolishing nasty things arriving on your doorstep, but they also have a tendency to demolish things you wished they hadn't!