My student told me his mother has cancer, what do I do?

As an instructor, the best you can do is to offer your condolences and tell him to just ask you if he needs anything. For example, you could offer an extension on assignments. If he needs some time off from lectures, maybe a classmate who takes good lecture notes will agree to make a photocopy, or you could get the lectures to be recorded for him.

Your university might also have a policy that allows students to withdraw from the course and receive a refund of fees without penalty to grades: it would be worth finding this out and advising your student if this is possible. Depending on the severity of the illness and how much it is affecting your student, he might wish to take fewer (or zero) courses for a while.

If the course is nearly finished, perhaps an aegrotat (compassionate consideration) will be applicable to the final exam. But neither an illness in the family, nor a bereavement or any personal physical or mental health issue can excuse a student from having to learn the material and complete assessments in order to pass a course. He will still have to demonstrate mastery of most of the material.

Just be compassionate, and as flexible as you feasibly can. Nobody could ask for more.

I imagine that most universities will have policy on this, and professionals who are trained to help. Apart from "find out the policy", IMHO unless you know the student well personally and are confident in your ability to deal with things like this (which the fact that you are asking this question suggests you are not) then all you should do is express sympathy and,

• ask whether they've told anybody else at the uni. If not, with their permission, consider informing whoever has overall responsibility for their academic progress (eg head of dept, director of studies, etc)
• make sure that the student is aware of whatever counseling services your institution offers
• research for your own info what arrangements can be made for extensions to deadlines, or consideration of circumstances when exams are marked, both for the current situation and in the event that the parent dies.
• make it clear to the student that allowances can be made (assuming this is the case), and that they should not be hesitant to speak to you if they feel that the situation is affecting their academic performance. No need to be specific for now - if the student is worried about this then just knowing that there are "options" may reduce the stress that they feel.

NB I have no particular qualification to comment here; once again, your uni probably has people whose job it is. If in doubt, consult them.

You might encourage him to reach out to other resources at the university. I imagine your university has counseling or psychological services, a chaplain, and the student may have an assigned advisor who can help the student understand their options, and provide professionally trained support.

I think the comments about offering certain accommodations, as you think appropriate, is generous and reasonable.