Von (generally in small case only as von) is a German preposition which approximately means of or from.
When it is used as a part of a German family name, it has in more recent times often been indicative of a member of the nobility. At certain times and places, it was illegal for anyone who was not a member of the nobility to use von before their family name. However, historically the "von" particle was a common part of names and was widely used also by commoners, e.g. "Hans von Duisburg" meant Hans from (the city of) Duisburg.
The abolition of the monarchies in Germany and Austria in 1919 meant that neither state had a privileged nobilty, and both had exclusively republican governments. In Germany, this meant that in principle von simply became an ordinary part of the names of the people who used it. There were no longer any legal privileges or constraints associated with this naming convention, although in practice, many people with von in their names are still listed in telephone books and other files under the rest of their name. (e.g. Ludwig von Mises would be under M in the phone book rather than V.)
In Austria, in contrast, not only were the privileges of the nobility abolished, their titles were abolished as well. Thus, for example, Friedrich von Hayek became Friedrich Hayek in 1919 when Austria abolished all indicators of nobility in family names.