Putting on a four-cornered garment bearing tzitzit is the next mitzvah that men do in the morning after netilat yadayim (hand-washing). The mitzvah of tzitzit is mandated by the verses from Numbers 15: 37-41. The Torah there requires that one of the strings on each corner be dyed in techelet, an azure-coloured dye. (Today there is still uncertainty over whether we can correctly identify the type of sea snail from which techelet is derived.)
The Mishnah Berurah comes out strongly against the practice of surreptitiously tucking tzitzit into your trousers, saying that this is an insult to the mitzvah and that if you had an object bearing the imprimatur of the king, then you would proudly and openly display it. He recommends putting the strings into your pockets if you are worried about the reaction of non-Jewish work colleagues.
Tzitizit are meant to serve as a reminder. The danger with reminders is that one can remember to remember, but still forget what it is that one is meant to remember. The Torah says it is to remember all the mitzvot and do them. The Gemara poetically describes how the blue of the techelet recalls the blue of the ocean that reminds us of the blue of the sky that is a hint of the Throne of Glory.