Tzitzit by way of commandment are mentioned in two places in Torah:
Again the Lord spoke to Moses, saying, “Speak to the children of Israel: Tell them to make tassels on the corners of their garments throughout their generations, and to put a blue thread in the tassels of the corners. And you shall have the tassel, that you may look upon it and remember all the commandments of the Lord and do them, and that you may not follow the harlotry to which your own heart and your own eyes are inclined, and that you may remember and do all My commandments, and be holy for your God. I am the Lord your God, who brought you out of the land of Egypt, to be your God: I am the Lord your God.” Num 15:37-41
“You shall make tassels on the four corners of the clothing with which you cover yourself.” Deu 22:12
The color of the tassel is not commanded, other than to include a blue thread in the tassels of the corners. There is some indication in rabbinic literature, that blue especially signifies God. They say that when the pillar of fire led the children of Israel through the wilderness, that it was a blue flame; and when Moses and the elders saw a vision of God on His throne, His throne was on a pavement, as it were, of transparent sapphire (Exo 24:10).
Moreover, the history of the ancient world itself might lend some insight into the custom of wearing tzitzit.
“Thus it seems that “zizziktu” represent not only the person they belong to but also show their authority. It seems that royalty would wear “zizziktu” that were distinguished from those of others. Prophets would also wear “zizziktu” that were also easily recognised. It has been suggested that the differences might be in how they were tied or their colour. Various clans, tribes and professions might have been distinguished by the variety of the “zizziktu” worn. This would help explain why Prophets often seemed to have little problem in gaining access to the King in Bible accounts.” — Tzitzit and Cuneiform Tablets, flickr.com
So blue, as God’s color, indicates that the wearer of tzitzit in which is tied the blue thread, belongs to God, and so remembers His commandments when looking upon them, because His is the authority.
There is a debate in Messianic circles today as to whom the command to wear tzitzit applies. The Orthodox Jews say it only applies to males, and many in Messiah follow suit. The command in Torah is to the children of Israel. This is in Hebrew, b’nei Yisrael. The root word ben is defined variously in Scripture as “son, grandson, child (both genders), children (both genders), member of a group.” Often when singular it means son, but when plural can mean the all- inclusive children of both genders. In Num 15:37-38, it is plural. Many times the phrase “children of Israel,” b’nei Yisrael, appears in Torah when the command can be clearly seen to apply to both genders. For example, in Lev 11, the Lord commands the children of Israel (b’nei Yisrael) to partake only of clean animals, and to not partake of unclean animals. This command is accepted throughout the Messianic community (and also in Judaism) to apply to both genders, and not the men only. Please see Women Wearing Tzitzit to examine the historic debate among the rabbis as to the application of this commandment, as recorded in the Mishnah and rabbinic literature. So, let every one be fully convinced in his own mind. I myself do wear tzitzit in many colors to match my clothes, but all have the same blue thread in them.