Blue is a reminder of the blue thread that was once added to the fringes (tzitziot.)  The commandment is explicit in the Book of Numbers: "Let them attach a cord of blue to each corner [of the garment]."  A blue thread is no longer added to each fringe because the source of that dye is no longer known; instead blue has become the colour of the tallit stripes.

The Talmud indicates that blue was a favourite colour of the Jews because the Mediterranean, the largest body of water near ancient Israel, casts a blue hue. Tradition holds that the colour is a reflection of G-d's throne, which is believed to be decorated with sapphires.