[86a top] Rashi: Slaves used to wear special signets to identify them as belonging to their owners.
R’ Rosner quoting Rashi [in Shelach]: Hashem gave us the Mitzva of Tzitzis by end of the plagues.
Orech Chaim & R’ Soleveitchik: Tzitzis is connected to leaving Egypt (even in 3rd paragraph of Shema) since in Egypt we wore markings as slaves (and were ‘branded’ with numbers and yellow Jewish Stars in the holocaust), when we became freed, Hashem gave us new identifiers to wear to show our physical freedom but spiritual servitude to Hashem with our Tzitzis.
R’ Volby: Tzitzis remind us of all the Mitzvos [number of commandments = the total strings + knots]. Just like when someone drowning has a life preserver to grab onto, so to are our Holy strings (like the Mitzvos) there for us to be spiritually saved, by grabbing onto them.
D-E-ep Thoughts: We should not only always wear our Tzitzis out because the commandment is “to see them,” but also because we want to be reminded by others and through ourselves of our constant connection to Hashem and to show our loyalty and thanks to Him for everything He has done for us and for all that we constantly have.