How do Tzitzis remind the wearer of all the Mitzvos?
Rashi: Because the Gematriyah of "Tzitzis" (600), plus the eight threads and the five knots equals 613. 1
Ramban (citing Menachos, 33b): It is the T'cheiles 2 thread that reminds the wearer of all the Mitzvos, in that 'T'cheiles resembles the sea, the sea resembles the sky (in the evening) and the sky resembles Hashem's Kisei ha'Kavod.
Seforno: By reminding him 3 that he is an Eved Hashem, 4 who accepted His Mitzvos with a curse and an oath. And in so doing, one frees one's mind from vain, mundane thoughts and concentrates on the greatness of Hashem and His kindness and goes on to performing all the Mitzvos 5 with love and awesomeness.
See Ramban's objections to this explanation, and Sifsei Chachamim.
Ramban: So-called because it is the ultimate color - since, from a great distance, every color adopts the color of Techeiles. According to Kabalah, the Name too, resembles the Midah 'Kol' - See Ramban, Bereishis 24:1 DH 'Aval Acherim'.
Seforno: Since they are a badge of Avdus - similar to the seal of slavery that a slave wears.
As stated in the next Pasuk.
What does the Torah mean when it writes "ve'Lo Sasuru acharei Levavchem ve'Acharei Eineichem asher Atem Zonim ... "?
Torah Temimah (citing B'rachos, 12b): "Acharei Levavchem" - is a La'av against heresy and "Acharei Einechem", a La'av against immorality.
Ramban (citing the Sifri): "Acharei Levavchem" - is a La'av against heresy and "Asher Atem Zonim", a La'av against idolatry that result from from delving erroneously into the Midah of Techeiles 3 - which Kabalah refers to as 'Kitzutz bi'Neti'os'.
Seforno: "Acharei Levavchem" is a La'av against seeking wealth and Kavod through theft and "Acharei Einechem", against pursuing the physical pleasures that one sees.
Rashi: As we learned earlier in the Parshah (13:25 "Vayeilcu mi'Tur ha'Aretz", which explains why the Torah places it here in the same Sedra as the Meraglim heart first is because the eyes see what the heart wants them to see..
The reason that the Torah inverts the order and mentions the heart before the eye is because the eyes see what the heart wants them to see.
And what are the connotations of the words "asher Atem Zonim achareihem"?
Seforno: it means that one turned one's logical mind towards them, to stray from the path of eternal life to that of destruction and death.