Students insist that 42 - 15 = 33. They get confused when comparing quantities like 390 and 309. And they really aren't sure how to describe the difference between 39,000,000 and 39,000.
Place value is the bane of the elementary teacher's existence, isn't it? Conceptual understanding of ones, tens, and hundreds needs to begin so early in a student's career, and then builds every year. It's so vital to a student's understanding of other math concepts that many math misunderstandings can be blamed on a student's gap in place value understanding. It affects an understanding of large numbers, rounding, and as students get older, multiplication and division.
A fun way to highlight what our Base Ten system represents is to experiment with other bases. Let's say, for instance, that we had a Base Six system. A few days of experimenting with counting in Base Six (1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20...) adding in Base Six, even multiplying in Base Six (that's hard) would really give students a reminder of what these different "places" our large numbers represent. Even as a math major, I never explored concepts of numbers like this until well into my college career, and it's an excellent way to teach and review place value understanding!