Thingvellir is fascinating for two reasons:
l) political..it is the site of the world's oldest Parliament, the Althing. It was first convened in 930 and continued to convene in Thingvellir as a legislative assembly and judicial court until 1844 when it was moved to Rekykjavik. The site, called Parliament Plains, is much revered by the people of Iceland.
2) geological..this area is a part of the North Atlantic rift system. Most of the rift system is on the sea floor, but Thingvellir is one of two sites on Earth where the effects of two major plates (the North American plate and the Eurasian plate) drifting apart can be observed. As the two plates pull apart, a rift valley is formed, as you can see in this photo. The valley walls are moving apart at a rate of about 7mm per year and the floor is subsiding at about 1mm per year. Obviously, this is an area of much volcanic and earthquake activity and quite fascinating to observe and walk through.