The rule of wearing threads on the corners of one's clothing is a commandment found in the Bible itself:
The Lord said to Moses:
Speak to the children of Israel and tell them to make fringes on the corners of their garments for all time; have them attach a thread of blue to the fringe at each corner. And it shall be a fringe for you to see and remember all God's good deeds and do them and stray not after your heart and after your eyes to sin. Remember and do all My commandments and become holy to Your God. I am the Lord Your God who took you out of the land of Egypt to be Your God. I am the Lord Your God. (Numbers 15:37-41)
As a reminder of the blue thread which was once required in each corner of the prayer shawl, we traditionally include either blue or black stripes in the prayer shawl itself.
The blue stripes in the Israeli flag was put there as a reminder of the blue stripe that was traditionally put in the prayer shawl.
According to Jewish tradition, the act of putting on a prayer shawl has religious merit only if it is put on in the light of day.
In the Book of Ruth there is a beautiful scene on the threshing floor. Boaz covers Ruth with a corner of his garment. (In those times, the threads were attached to garments rather than to a prayer shawl and he covered her with a corner of his garment that had the threads attached to it).
A prayer shawl found in the Bar Kochva caves (132 of the common era) has threads which are of indigo dye, which is indistinguishable from the required blue dye, but not the correct dye prescribed for the making of the blue threads.
In the Israel Museum in Jerusalem, in the building which houses the Dead Sea Scrolls, there is a small Bar Kochva exhibit. In it, one can see the remains of that prayer shawl.
On the subject of Bar Kochva, anyone reading this and interested in Jewish history should look into this era if you are not already familiar with it.
To summarize it, the Romans took control of the Mediterranean Area after the Greeks, and were far too great a foe for the Jews. They destroyed the Second Temple in the 60th year of the Common Era.
Seventy-two years later the Jews tried to make a comeback, headed by Bar Kochva.
We have the dry climate of the Judaen desert to thank for the preservation of written documents and artifacts from this heroic period of Jewish history. Jews struck motifs of the Second Temple Period coins over the Roman coin motifs of the time. These Second Temple Period motifs included date palms, grapes, grape leaves, the palm frond, etrog, myrtle and willow, the harp of that time, the Holy of Holies of the Second Temple, and the seven species: barley, wheat, date, olive, pomegranate, grape and fig.
The coins of this period can be seen at the University of Haifa Hecht Museum in Haifa, Israel. The Hecht Museum also houses an exhibit of the sea-faring Phoenicians where one can see examples of the sea snail (the chilazon in Hebrew) from which the blue dye for the threads was made.