A bit intuitive, but maybe it'll help. Let's say you want to learn some new language. How do you learn? instead of learning the rules in a course, you use examples. Specifically, TV shows. So you like crime shows, and you watch few series of some cop show. Then, you take another crime show and watch some series form that one. By the third show you see - you know almost everything, no problem. You don't need the English subtitles.

But then you try your newly learned language on the street on your next visit, and you realize you can't talk about anything other than saying "officer! that man took my bag and shot that lady!". While your 'training error' was zero, your 'test error' is high, due to 'overfitting' the language, studying only a limited subset of words and assuming its enough.