Weltlich sein - to be of the world
The english “to be of the world” doesn’t really translate nicely word by word, because it may loose its original meaning in the process. “Von der Welt sein” doesn’t hit the point the english original does.
The pure genetive “jemand sei der Welt” or in its old from “jemand sei der Welten” sound very strange to the German reader, even this being comparable to “to be of the devil” (“des Teufels sein”), which is well understood in German.
But language tradition was different in Germany, of course, so that the current translation to “weltlich sein” is better perceived and understood as a state of being oriented to the world, not to the Lord. In other words: People that are “of the world” (“weltlich”) put worldly things first and only after that take care of their relation to God, if there is any.
So “being of the world” has nothing to do with inheritance or birth. All human beings are born into this world, made of the elements of this world. Even Jesus himself. But what matters to God is our relationship to him, which is completely immaterial, outside of this world and by nothing depending on anything from this world, but our heart and mind.
People that are not of this world are by no means irrational or funny, they just have priorities that always put God first. They subjected themselves to their relation to God as their heavenly father with every consequence this might mean to their life. Because of this attitude, somebody that is “not of this world” (“nicht weltlich”) will never do somethings that his father in heaven would not agree to. God is their only authority.