I think you’re close - someone well travelled is someone who has a broader view of how the world works than just the one country they were brought up in.

That happens when they go to countries and actually experience them. I’ve just been to the Canary Islands for a week - I went airport to hotel, sat beside the pool for a week and then went home again. This was lovely and relaxing (which I needed) but did nothing for expanding my cultural horizons.