When you get a virus, your immune system develops a response to it. This response goes away over decades, or never, and it's why you're generally immune to any virus you've survived. (There are two important exceptions. "The flu" keeps coming back because it isn't actually a single virus at all: it's an entire family of related viruses. Each year's flu tends to be 1-3 separate epidemics. Colds and other "recurring illnesses" are like that, too: a single name for a huge bestiary of different illnesses. And a few viruses like HIV are so hard to treat because they can rapidly edit themselves, changing their outer structure until your immune system can't recognize them.)
This means that your immune system ought to contain a record in it of every virus you've ever had. And that's exactly what this research team showed. Not only did they show it, but they figured out a way to build a test which, from just a small sample of your blood, can produce a list of every virus you've ever had -- whether you showed symptoms or not.
At least, that's the short version that the press seems to have gotten. If you read the article itself (http://www.sciencemag.org/content/348/6239/aaa0698
), you'll see that it's a bit more subtle. What they actually do is set up a collection of known viruses -- 206 different viruses and over 1,000 different strains -- and can automatically scan a tiny (1µL) blood sample against all of them, seeing which ones its immune system responds to. So this won't detect any viruses or strains which they didn't put into the test; it won't pop up and say "oh hey, there's some completely unknown virus in here, too."
This is one of those discoveries that could really change the way we do many kinds of science -- it's a big enough change that it's hard to predict what it might mean. For example, imagine if we got a viral history of a million people. We might discover that some particular pattern of viruses was connected with something seemingly unrelated: a kind of heart disease, perhaps, or Alzheimer's. It's quite likely that there are many connections like this; for example, the relationship between HPV and cervical cancer is the reason so much effort went in to making an HPV vaccine. Prior to that discovery, thousands of people were dying every year and nobody knew why.
One important question is whether a very broad survey of people's viral histories ("viromes") is a good idea, or whether it might have dangerous consequences for the people involved -- in much the same way that people have reason to fear widespread genetic testing.
I suspect that it will prove safe, because a person's virome doesn't appear to be strongly personally identifying: if you had certain strains of the flu, and a certain strain of chicken pox, then someone could probably guess which general area of the world you grew up in, but not much more.
On the other hand, viruses such as herpes-2 and HIV carry strong social stigma, and this would be reason for people not to want to broadly publicize their personal viromes. So some care will have to be taken with large-scale studies. However, the potential health benefits to this are enormous; enough that we should find a way to do it.