Tzitzit: Hidden or Revealed?

Is looking at the tzitzit during the mitzvah, a part of the mitzvah itself, or an additional element, separate from the actual mitzvah of tzitzit? And what is the meaning of the word ‘tzitzit’? Analyzing the Rebbe’s chakirah on the definition of the mitzvah of tzitzit, and its ramifications with regards to the different customs on how to wear the Talit Katan — with the tzitzit hidden or revealed.