‘Suck it up’ is used when you need to force or convince someone to do something that is difficult or unpleasant. A parent can say this to a child. A boss can use it with a direct report. Your best friend may want to convince you that there is no other way out.
 
Here are a few dialogues that will show you how to use it in context. As you can see, it is the same as saying ‘ you just need to do it!’ or ‘bite the bullet’.
  Dialogue 1 A: I am so tired. I don’t want to study.
B: You have a test tomorrow. Just suck it up and hit the books.
 
Dialogue 2
A: I don’t like going to family reunions.
B: Neither do I. We just have to suck it up and make Mom happy.
 
Dialogue 3
A: The big boss has just invited us to dinner with the clients next Monday.
B: Do I really need to be there?
A: Yes, I am afraid you do. Suck it up and put on your best smile. He needs our support with closing the deal.