Why did the Israelites have a blue line of thread on the hem of all their garments?

Answer 1

Fringes and tassels. God commanded the Israelites to make fringed edges on the skirts of their garments, with a blue string above the fringe. This seems to have been peculiar to Israelite dress and provided a visual reminder that they were set aside as a people holy to Jehovah. It would keep before their eyes the fact that they should obey Jehovah’s commandments. (Numbers 15:38-41) Tassels were also to be put on the four extremities of their clothing; possibly this had reference to the four corners of the mantle. (Deuteronomy 22:12) The hem of the high priest’s blue sleeveless coat was fringed with alternate golden bells and pomegranates of cloth material.—Ex. 28:33, 34.

The unique fringe of the Israelites’ dress was intended to remind them that they were a people set apart to worship God and to obey his commandments. Why? So that they would remember Jehovah’s commandments, obey them, and “prove to be holy” to their God. (Numbers 15:38-40)

Answer 2

this was to remind them to keep the commandments. I'm not sure why blue was used for that purpose, but it is interesting to note that even today, blue is considered symbolic of loyalty.

The shade of blue was called techelet, and could only be made by a certain dye that was rare, and the method for making it has been lost, I believe. That is why there is no blue thread in the fringes worn by Jews today. However, you will notice the theme of a blue thread has been kept symbolically. That is seen in the blue stripes on the prayer shawl, and even in the Israeli flag.

Answer 3

When Moses first came down from the mount with the tablets of the 10 commandments they were blue Sapphire stones that came directly from God. So the blue piping is the acknowledgment of the 10 commandments of God. His law and His character and the character of His government.