Question 1: Is the the Apocalypse?
No, it is not. This earthquake occurred in a region known as the Central Virginia Seismic Zone, where small earthquake activity has been commonly noticed since at least 1774. The largest previous earthquake in the Central Virginia Seismic Zone was a magnitude 4.8 in 1875. More recently, a magnitude 4.5 earthquake struck the Central Virginia Seismic Zone on December 9th, 2003. This will undoubtedly be the largest recorded earthquake within the Central Virginia Seismic Zone; however, if its current designation of a magnitude 5.8 holds, it will not be the strongest earthquake in the history of Virginia. That distinction belongs to the Giles County earthquake of 1897, a magnitude 5.9 centered near the West Virginia border that was felt all the way in Cleveland, Indianapolis, and Atlanta.
Question 2: How worried should I be about aftershocks?
Probably not too worried, but be cautious. From a cursory look through USGS earthquake records, previous Central Virginia Seismic Zone earthquakes (the 1875 and 2003 earthquakes) show little record of significant aftershocks. At the time my writing, there have already been two aftershocks, a magnitude 2.8 at 2:46pm Eastern Time and a magnitude 2.2 at 3:20pm Eastern Time (Figure 1). An aftershock would likely need to be at least magnitude 3 to be felt in the greater D.C. region. For comparison, the Giles Country Earthquake of 1897 produced aftershocks for a week after the earthquake, although every earthquake is different and we can't be sure of what features translate between earthquakes.
Question 3. Why did this happen? I thought earthquakes only occurred in California.
Earthquakes can occur anywhere there are faults, regardless of the age of the faults. Many faults are concentrated today at plate boundaries, where large portions of the Earth's crust join and grind against each other. California is the first and foremost example of this; the Pacific plate meets the North American plate at California, and the geologic happenings associated with this juncture lead to a lot of seismic activity. The Eastern Seaboard of the US is a geologically calm area today, but that was not always the case; when the Appalachian Mountains formed around over 200 million years ago, there was an active plate boundary just off the East Coast. Faults existed all along the East Coast then, and many of those faults are still preserved in the bedrock today. We don't know what triggers them to reactivate, but occasionally they do. And because they happen so less frequently on the East Coast than in California, we are always in for a surprise when they do occur.
The obligatory hands-on-the-face, "what-the-heck-is-going-on" East Coaster in an Earthquake look. Courtesy of New York Times.