Problem applies to a question or difficulty calling for a solution or causing concern. Dealing with a moral or social problem: Has financial and emotional problems.
There are nine meanings listed in oed's entry for the noun problem, three of which are labelled obsolete. A problem is a question or puzzle that is intended to be solved or to be deeply thought about. Your teacher may present a problem to the class so you can use what you’ve learned to.
A problem is a situation that is unsatisfactory and causes difficulties for people. A problem can be defined as a situation or an issue that needs to be resolved or dealt with.