A Slovak proverb (Koľko rečí vieš, toľkokrát si človekom, literally translated "as many languages you know so many times you are a human", or, idiomatically, the number of languages you know is the number of times you are human).
I can attest from personal experience that this proverb is very true. My life would have been quite different had I not taken the time to learn many languages, and probably had I not started at an early age.
In my early teens I read books by a 19th Century German writer Karl May whose hero had the rule of always learning the language of any country he was about to visit. I made it my own rule and followed it with very few exceptions.
The big difference between knowing and not knowing the language of a country you are visiting is that of being just an outside observer (as if watching a very realistic movie) and that of being able to interact with the local people. By interacting, I mean a lot more than just telling a waiter what you want to eat! Rather, I mean becoming one of the people.
Knowing the language means you can learn about the culture of the country you are visiting, about things that matter to them--even things you had never thought of before, about their customs, about their world views, their philosophy, even their prejudices (and, you will gain an amazing insight into your own prejudices that you never knew you had).
I have not only visited many countries, I have lived in quite a few. I learned from the people of each and every one of them. All it took was learning their language and, of course, using it. My attitude about language has indeed made me a human many times over.