The phrasal verb 'come through' has a number of meanings and can be used in a variety of contexts. 'Come through' can mean to receive something official, such as results or information. So you could wait for the results of an important exam to 'come through' or wait for medical test results to 'come through'. When something 'comes through', it becomes visible or apparent to others. So, if you are upset about something, it might 'come through' in your voice, for example. If you add spice to something you are cooking, you hope the flavour will 'come through'. If you 'come through' something, it usually refers to surviving a difficult ordeal or overcoming a hard time in your life. If you 'come through' an illness, it means you have recovered. Some people manage to 'come through' depression, poverty or a death in their family. When you 'come through' for someone, it means to help someone in some way.
Additional examples with 'come through' are:
You ask your niece which university she wants to study in. She says,
"I am waiting for the university offers to come through before I make a decision."
Your French friend speaks English really well:
"Your French accent only comes through when you are angry or upset."
Your family are always ready to help when you are in trouble:
"My father always comes through for me when I am in a difficult situation. I can always depend on him."