As I understand, you are only beginning your graduate studies. At this stage you should get a problem from your adviser, a problem that you are likely to solve. If you want to become a professional mathematician, you should publish regularly, and for this you need problems which you are likely solve in reasonable time. What kind of problems you are likely to solve, you will gradually learn from experience. But in the very beginning, rely on the experience of your adviser.
But of course, you should also learn about "big and famous" problems, and think about them too. Then, if you are lucky, you have an idea how to make a progress in one of them.
My main advise for the beginner: choose a right adviser, and do what s/he recommends. In the remaining time, read and think on other problems.