During the last 5 months I made observation regarding my inner mind process. The inner chatter which most people know during their day disappeared completely in my mind. I practiced mindfullnes during my day and meditated as well. Is their a specific term in Buddhism which refers to achieving a quite or calm mind?
One could call it jhāna or dhyāna which is the meditation with a calm mind. You are on a great path. Perhaps you want to meditate on the heart sutra where it says:
"No suffering, no origination, no stopping, no path, no cognition, also no attainment with nothing to attain. "
The moment where you recognize a calm mind (the absence of something) as achievement, the ego crawls back up and claims having attained something. The true you is just about to get this ego to quite down. As you begin to research terms and more about having attained this great achievement you might create artificial distance again. Always remember that you are neither the mind nor the body.
A quitened or a calmed mind is an important and a dangerous milestone. It is important because it is a mark of your concentration that the mind's chatter has quitened down. It is dangerous because it is not the final stage- things change and the chatter may come up again and you may start despairing when that happens and so generate more misery.
The term for it may be one of the four jhanas or the stage of rapture/bliss. They are all intermediary stages. But it would be better if you further read on these stages, since only you would know the precise details of your meditative progress.