I think this quote does make sense, but it definitely can be confusing!
When you're learning a new language, you are forced to think about the very basics of how that language is structured from the smallest parts of words to the syntax itself. When you do so, you become aware of the structural elements of language that you may not have noticed in your own language that feels more innate to you. Learning a new language is always full of discovery--you may notice new ways of thought modeled in another language or even a new word for feeling you had never quite been able to describe. Therefore, when you learn a new language, your brain can really know your own language through a new lens. You may notice things in it you had not before, become more critical of the structures in your own language, or adopt elements of a different language for your own. You may not truly know your language unless/until you have something else to compare it to.
Hope this helps!