I have lived abroad and travelled abroad, and I am not convinced that travel really does necessarily help you learn these things. However, let us look at how travel abroad could potentially help you to learn them.
Travel abroad could help you to learn confidence, particularly if you are a teen or young adult without a lot of life experience. When you travel abroad, you have to deal with a number of new situations. If you are travelling without your parents, you have to deal with all of the situations more or less on your own. When you do so successfully, you gain confidence.
If you do it correctly, travel abroad can also help you understand other cultures better and see the world from a global perspective. Please note that this will not happen if you just go stay in hotels and never interact with people from other cultures except to buy things from them or give them your order in the hotel restaurant. If you actually get to go out and interact with people from other cultures on their own terms, you will come to know more about them. You will see something about how they act and maybe even get to understand how they think. If this happens, you will be able to think about the world from a more global perspective.
In these ways, travel abroad can teach you things that you would not otherwise learn.