If one wears a four-cornered wool garment, there is a biblical commandment to place a Tzitzit on each of those corners, and a Rabbinic commandment if the garment is something other than wool. In order to be able to fulfil this Mitzvah, many men wear a Tallit Kattan. [The regular Tallit is worn for this reason as well, although there is an added virtue of being wrapped in a Tallit during prayer]. The Shulhan Aruch (O.H. 8:11) states that the essence of the Mitzvah of a Tallit Kattan is that it be worn above one’s clothing so that one always sees it and remembers the commandments of the Torah. The Arizal, on the other hand, says that the Tallit Kattan should be worn underneath one’s clothing and this is the pervasive custom.
Regarding the actual strings of the Tzitzit, the Magen Avraham (O.H. 8:13) writes that based on the Gemara the strings should be placed outside of one’s clothing and should not be like those who stuff them into their pockets out of embarrassment. Those that follow the Arizal’s opinion say that even the strings of the Tzitzit have to be on the inside and they explain that the Magen Avraham simply meant that the strings should not be placed in a pocket but should be loose and underneath one’s garments.
Rabbi Moshe Malka (Mikve Hamayim, vol. III, §1) says that the original Moroccan custom was that the Tzitzit would be worn underneath one’s clothing and would not be exposed, and this was the custom among many Sephardic communities. Similarly, Rabbi Shalom Messas (introduction to Petil Techelet) says that the Tallit Kattan was worn day and night, but it was never observed that ordinary people or Torah scholars would place their Tzitzit on the outside. Granted that many men at that time wore the traditional Djellaba, which was not conducive to wearing the Tzitzit strings on the outside in the first place, nevertheless it was not the custom. This is also the opinion of Rabbis Ezra Attia, Yehuda Tzadka, Mordechai Sharabi, Ben Zion Abba Shaul and others.
Rabbi Ben Zion Abba Shaul (Or LeZion, vol. II, ch. 2, § 2) and Rabbi Ovadia Yosef (Yehave Da’at, vol. II, § 1) point out that if one studies in a Yeshiva or is in a community in which the practice is to wear the Tzitzit strings on the outside, one is permitted to do so. Furthermore, if wearing them on the outside gives one encouragement to grow spiritually, especially if one lives among those that are less observant, then it is appropriate.
Summary: The Moroccan custom is for the strings of the Tzitzit to be worn underneath one’s clothing and not to be exposed. There are circumstances in which wearing them on the outside is permissible.