Being able to "justify" an action or decision means that you're able to feel or explain why it's OK.
There are some things that you can't justify:
I like them, but I just can't justify spending that much on a pair of jeans.
But if you can think of a reason why it's OK, then your're able to justify it:
I could justify spending that much on them if I was able to wear them to work as well as on the weekends.
In general, "justifying" ideas means thinking of reasons to explain why you did something, after you already did it or wanted to do it. Usually "justifying" actions and decisions has a little bit of a negative feeling attached to it:
Don't try to justify what you did! You knew that what you were doing was wrong.