How are you doing?
--Fine.
How are you doing?
--Just fine.
In this context, the word "just" makes the answer "fine" a little bit stronger. It is similar to "really" in these greetings:
It is wonderful to meet you.
and
It is just wonderful to meet you. = It is really wonderful to meet you.
The just or really usually expresses a stronger emotion on the part of the speaker. Or it could just be politeness.
In reality, the greeting with or without the "just" is practically identical and not something a beginner needs to worry about. If you are unsure whether to use "just," I suggest you don't use it.