Your worldliness means that you've had enough experience, through travel and meeting different kinds of people, that you understand the way the world works.
Use the noun worldliness to talk about a person's awareness of and connection with the larger world. It implies a certain amount of style and poise as well, a graceful, knowing way of moving through the world. As a child, you might admire your older cousin's worldliness as she travels across Asia. The adjective worldly comes from the Old English woruldlic, which combines woruld, "human affairs or the world" and gelic, "like or similar."