The Torah tells us (Bereishis 2, 25) that before Adom and Chava ate from the eitz hadaas they were not embarrassed by their lack of clothing. Rashi explains that they were not aware of the concept of tznius which enables one to decipher between good and bad. Rav Wolbe (Shiurei Chumash) points out that this explanation of Rashi reveals a novel approach to defining the term "tznius." Tznius is the manner by which one deciphers if his actions are good or bad.
How can one know the true motivation for his actions? Rav Yeruchom Levovitz would say that a person has to familiarize himself with the many faces and colors of the yetzer hara. Although one might feel a great desire to perform a specific mitzvah, he must be able to discern if the surge of adrenaline is coming from his yetzer tov or from his yetzer hara. Performing a mitzvah is commendable; but it should not come at the expense of a greater or more timely Torah obligation. As Rav Yisroel Salanter would say, "The yetzer hara doesn't mind if one says Tehillim the entire day - as long as he doesn't sit down to study Torah in depth."
With this we can understand the Gemara at the end of Meseches Makos (24a) which discusses that pasuk, "What does Hashem request of you but to do justice, love kindness and walk modestly with Hashem." The Gemara tells us that to "walk modestly with Hashem" refers to the proper participation in funerals and marriages. The Gemara concludes that if these things - which are normally performed publicly - must be done in a modest manner, how much more so must we ensure that those things that are meant to be done privately, be carried out modestly. In other words, the way to gauge if the justice and kindness are a true fulfillment of the commandment is to determine whether they would have been performed in the same manner even when far from the eyes of any onlooker.
Tznius is not just an inconspicuous manner of dress. It is an inconspicuous manner of living. If the actions which one performs publicly would be performed in the same way inconspicuously behind closed doors, then one can be confidant that he has fulfilled his obligation in the sincerest manner!