If something is "up to you", it means that it's your responsibility. You are the person who has to do it. We use the phrase "it's up to ___ to ___" to communicate that it's important for a people to do something themselves, rather than relying on someone else to do it. 

It's up to each of you to make sure that you fulfill all of your graduation requirements.

If we get a dog, it's up to you to take care of it. Understand?