Numbers 15:39

You will remember all of Adonoy’s commandments. As the numerical value of צִיצִית is 600, and the eight threads and five knots equal 613.

And you will not search after [the desire of] your hearts. This is similar to “from spying the land.” The heart and eye are the body’s spies, bringing it sins. The eye sees, the heart lusts, and the body sins.

And this shall be to you a precept for fringes, that you may look upon them at the time when you dress yourselves daily, and remember all My commandments to do them, and not go aside to wander after the imaginations of your heart and the sight of your eyes, after which you have gone astray.

And it will be to you for fringes. Anyone who has a garment with four corners is commanded to always wear it during the day, and not take it off, so that he shall remember. Those that pray with a tallis [only] during the time of prayer do so because of the verses they read during the Shema: “Make for themselves, tzitzis-fringes” and “And it will be to you for fringes.” In my view, however, one has a greater obligation to wear tzitzis at other times than prayer, so that he will remember and not err, and not commit a transgression at any time. During prayer, however, he will likely not transgress.

And you will look upon it. It is a commandment for the tzitzis to be seen.

After [the desire of] your hearts. The eye sees and the heart desires. The tzitzis are a sign that a person should not chase after his desirous thoughts and anything his eyes seek.

Which cause you to go astray. Someone who follows after his desires is straying from the service of his God.

Scripture states, and that ye go not after your own heart, (All) is the all-inclusive attribute it therefore contains all the commandments of the Eternal, and hence the Rabbis have said that the commandment of Tzitzith is of equal importance to the total number of the commandments (Beiur Ha’lvush to Ricanti, quoting the text of Ramban). in order that one should take care concerning it and not err through it. It is for this reason that our Rabbis have interpreted: 115; Berachoth 12a. “After your own heart. This refers to scepticism. After which ye use to go astray. This refers to idolatry.” That is to say, through the t’cheileth he should not think [in his heart] of any scepticism or idolatry, but it shall all be unto you for ‘tzitzith’ — that ye may look upon it, and remember. The Rabbis have also said: 115; Berachoth 12a. “After your own eyes. This refers to immorality,” similar to that which is written, I am He that knoweth, and am witness, saith the Eternal. The student learned [in the mysteries of the Cabala] will understand.
In the Midrash of Rabbi Nechunya the son of Hakanah it is stated with reference to the verse, and the profit of ‘eretz’ (earth) is ‘bakol’ (in all): “And what is the eretz? It is that from which the heavens were hewn, and it is the Throne of the Holy One, blessed be He, and it is ‘the precious stone,’ and ‘the sea of wisdom,’. — The Ma’or V’shamesh [a commentary by Shem Tob ben Gaon on the Cabalistic passages in Ramban’s commentary] continues, on this basis, to explain a basic law in the commandment of Tzitzith, namely, that it applies only at daytime and not at night. Thus he writes: “Hence [i.e., since the t’cheileth in the Fringes represents the all-inclusive attribute, and we are commanded to look upon it, and remember etc.] the commandment applies only at daytime and not at night, for at night physical features are indistinguishable and nothing can be seen in its entirety, while only at daytime the wholeness and perfect harmony of the t’cheileth can be seen and contemplated for its profound meaning].” and corresponding to it is the blue thread in a garment of Fringes, for Rabbi Meir has said: ‘Why was blue chosen? etc.’” [as quoted above].

והיה לכם לציצית, the string known as tzitzit serves to attract your visual attention. The word is used in a similar sense to Song of Songs 2,9 מציץ מן החרכים, “peering” through the lattices. I have found that Sifri on our verse explains the word in similar fashion, quoting above verse from Song of Songs.

פתיל תכלת, our sages explained the reason for the blue colour as designed to remind the viewer of the blueness of the ocean, which in turn resembles the blueness of the sky reminding man of the throne of G’d’s glory situated in the celestial spheres.(compare Sifri on our verse).

'וראיתם אותו וזכרתם את כל מצות ה, you will be reminded that you are G’d’s servants whose commandments you have accepted reinforced by oaths known as אלה and שבועה. This reminder will be due to your looking at the “fringes” that may be viewed as if their king had placed a stamp on your bodies confirming that the wearer is one of his subjects.

This in turn will lead to your ceasing to follow the inclination of your hearts and eyes to indulge your diverse urges, originating in your bodies. Without these fringes as a constant reminder of your purpose on earth, you would be likely to fall prey to these urges inspired by the evil urge.

This would eventually diminish the influence of your mind over your body to such an extent that it would lead to your premature death both in this world and in the hereafter.

וראיתם אותו, “when you see it, etc.;” since being able to look at the tzitzit when you wear them is of the essence, garments worn only at night are not required to have such fringes attached to them. This is also why a blind person is not required to attach fringes to his garments. In other words, the commandment to look at the fringes is meant for people able to see them. (Menachot folio 43). If you look at the fringes with the proper concentration it is considered as if you looked at the throne of G–d, which is supposed to look like wool dyed blue. Rabbi Meir, in describing the difference between that tint of blue from all other colours, said it is because it is closest to the blue of the horizon, which by definition is a reminder of the heaven beyond it. He bases this on Exodus 24,10 as interpreted in the Talmud, tractate Menachot, folio 10, where the elders are described of having looked at a Divine apparition which they described as looking like bricks made of sapphire. The colour of a sapphire is supposed to be just like the colour of the horizon. The sequence of three verbs in our verse, i.e. “you will see,” “you will remember,” and “you will do, i.e. perform,” explains the importance of this commandment and how fulfilling it will stimulate our heart and eyes to be loyal to G–d.

'וזכרתם את כל מצות ה, “you will remember all of the Lord’s commandments;” Rashi points out that the numerical value of the letters in the word ציצית is 600, (he is aware that the word is spelled defective, with one letter י missing, so that it is really only 590.) The word appears three times in the paragraph, once with the prefix ל, the numerical value of which is 30, so that we may consider these three words as all having been spelled perfectly. I have also heard that the manner in which some people arrange the fringes are separated from one section to another with knots and ringlets around each section, each of a different number of ringlets amount to a total of 613, so that the wearer is constantly aware that he is clothed symbolically in the 613 commandments. The Talmud in Menachot folio 39 goes into all the details.

ולא תתורו אחרי לבבכם ואחרי עיניכם, “do not follow your heart and your eyes in a lustful urge.” The Jersualem Talmud, tractate B’rachot chapter 1, halachah 5 describes the heart and the eyes as the principal agents of the evil urge within us.