how do you prove that you understand something?

What you want, when the university looks at your materials, is that they understand why *they* want *you*. That you want them is assumed. So write your statement with that in mind. One thing they want is to admit students to the course who really understand what the point of the course is and how it will enable them to achieve their own goals and develop the skills and knowledge they most want.

Write about why you are applying to this course and not some other course. What is so interesting about it? How will it help you achieve your goals? What strengths do you have that will enable you to do good work? Are there particular modules that you are eager to take? If so, what is it about those modules that excites you? Is there a lecturer there who recently published a fascinating book on basket-weaving at hydrothermal vents and whom you would love to learn from? There's a way to write this so that it's all just about "me, me, me," but by demonstrating that the specific course you are applying to is one that will excite and inspire you, you are letting them know that you are the kind of student they want to attract.

Make it clear that you did not pin up the list of courses on a dartboard and then pick which one to apply to by getting drunk, turning your back on the board, and throwing the dart over your shoulder to see where it hits. (While I am sure that that specific method is not a common one, I am familiar with situations in which post-graduate students in the US applied to programs/courses mainly because the university has a good reputation and because the most superficial discussion of the programs seemed to interest them -- and who discovered only after they were enrolled that the programs were completely unrelated to their own interests. In one program, where there were 3 or 4 such students in a cohort of about 12, they became incredibly disruptive because they refused to recognize that the material they were expected to master was appropriate to discuss in class meetings.)

Use your statement to let them know other things about yourself. For instance, if you are applying to a basket-weaving course at Fictional University, you might want to mention that your life-long dream is to be an underwater basket-weaver, and the fact that there are 3 optional modules dealing with basket-weaving in atypical environments (underwater in general, specific locations underwater such as coral reefs, and atypical environments more generally, including underwater in a fast-moving river and on the summit of Mount Everest) really attracts you. Or you might mention that the first year of the course is all about the basics of basket-weaving, and even though you earned an A* for basket-weaving at college, you appreciate a broad-based and rigorous training in the fundamentals of basket-weaving so that when you begin working underwater, you'll be able to do excellent work even if there are jellyfish floating nearby, threatening to sting you, and distracting you from your basket. Or perhaps Fictional U's basket-weaving class is not broad-based at all but focuses heavily on underwater basket-weaving (your particular area of interest), and you will be working in a bathtub, an Olympic-sized swimming pool, and a small pond in your first term, and progressing to weaving metal baskets while parachuting through thunderstorms (the current cutting edge of extreme underwater basket-weaving) by your final term, and you believe you have mastered the fundamentals sufficiently to dive right in to the underwater part.

You may want to talk about the range of jobs that a graduate of Fictional University's basket-weaving course might be able to acquire, and how your degree will prepare you to do exactly the kind of work you want. If most people who attend Fictional University come from very close to it, and if Fictional University is smack-dab in the middle of the closest thing to a desert that exists for thousands of kilometers, your desire to move to the coast to begin your career would be important; if you think (as 2/3 of the students do) that you will be able to beat out the other members of the course to obtain a job weaving baskets in decorative fountains, a local industry that can only employ 1 or 2 new, poorly-paid, basket-weavers each year, that indicates that you don't understand quite what jobs you may be *likely* to get.

Does that help at all?

The best way to demonstrate understanding is to have to teach or explain something.

So you are going to want to explain your understanding of the course topic, then how it relates to your life or goals.