To the best of my knowledge there were no advances in medicine and people were still killing each other. Why in the 800s were there suddenly too many people?
Historians in the 1800s and early 1900s thought that overpopulation may have driven viking raids because the sources said so—and perhaps because overpopulation seemed to be a cause of their contemporary problems as well. But modern historians are more skeptical. We now acknowledge that early medieval authors were every bit as coy as we are, so the overpopulation theory has become a matter of debate. At the same time, archaeological research has expanded dramatically, and archaeologists have focused especially on environmental factors, which are a pressing subject of inquiry given today's concerns about environmental change. So environmental factors have come to the fore.
When archaeologists and geologists identified a "warm period" just preceding the modern period, it was quickly assumed that this warm period allowed intensified agriculture and thus caused overpopulation in the subarctic—the spark for the Viking Age. The problem is that the more information we gain, the less we're able to associate this warm period with the period of colonization that began in the mid-800s. The medieval warm period is now commonly dated to about 950-1250. Although there is evidence for expanded agriculture during this time, there seems to have been no lack of available land, and "overpopulation" is no longer a pressing subject of inquiry.
So why did Scandinavians begin to emigrate? I'm actually not sure this is even the right question. It looks to me like beginning in the 700s there were migratory communities of Norse speakers that would raid or trade as opportunity allowed. You might think of them like modern ex-pats, but without a real political patria to hearken back to in Scandinavia; the slave-trading Portuguese of the early modern Atlantic might be another good basis for comparison. A number of political and economic factors encouraged these Norse-speaking wanderers to take root in Western Europe in the mid-800s. I've outlined some of my thoughts in this thread regarding the settlement of Iceland.