Pingvellir National Park is famous for two different reasons. First, it is where the Teutonic plates for Europe and North America come together. They are slowly pulling apart, part of what contributes to the volcanic activity in the country. There are many really cool geologic features in the area, long basaltic ridges that are pulling apart, wterfalls, lakes. It's beautiful.
The second thing it is known for, is that for 100's of years, this is where the early settler's gathered to govern them selves. One individual was the law giver. He would stand on the law rock and recite all their laws from memory. Clans would gather in various tents on the plains. Disputes were heard and settled, new laws made and there were even some executions.
This is known as the drowning pool. Sixteen women were executed by drowning here. The mean were usually beheaded.