It's the kind of thing native English speakers say, and people understand it once it's explained to them, but it's flawed logically. "the less you realize you know" sounds like your understanding of your own knowledge is reducing. But that's not what it means. "Less" doesn't go with the "realize" that it's close to in the sentence, but with the "know" that it's far from. A more verbose, but hopefully clearer, way of saying this is: "As you learn things, you see more of the-amount-left-to-learn than you were able to see before." The amount-left-to-learn hasn't changed size. You're merely now able to see more of it. For example, just learning that there's a library down the street (or a new website) means that there's now this new resource of information that I hadn't even been aware of before. The more I learn (the existence of the library) the more I realize there is left to learn (the contents of the library).

It is written the wrong way, but it may be intended to mean: "The more we study, the less we know." We don't know how much there is to learn until we study. After studying, we find how much we did not know, and how many more questions are left unanswered than ever before. The sentence contradicts its intended purpose. A more appropriate construction of this sentence could be from: "The more you learn, the less you realize you know" to: "The more you learn, the more you realize how little you know." I avoid using the "you" pronoun and may use "I," but prefer to be inclusive by using "we." Better yet, eliminate pronouns altogether: "The more I learn, the more I realize how little I know." "The more we learn, the more we realize how little we know." "The more that is learned, the more is realized of how little is known."