What is the significance of the number of coils on the tzitzit?

There are five (double) knots on each of the tzitzit tassels. In the spaces between these knots, one of the fringes – which is longer than the others – is coiled around the rest. Seven coils in the first space, eight in the second, eleven in the third, and thirteen in the fourth. These 39 coils have the same numerical value as "Hashem Echad" -- G‑d is One.

We start with seven coils and conclude with thirteen because when the blue (techelet) fringe was added to the tzitzit, it was coiled around the white fringes anywhere between seven and thirteen times. Techelet is sky-blue, (a constant reminder of the G‑d in Heaven who watches over our every action), and there are seven (spiritual) heavens. If including in the count also the six spaces between the seven heavens, there are a total of thirteen.

Perhaps the reason why the middle two spaces have eight and eleven coils is because G‑d's name (the Tetragrammaton) is divided into two parts; the first part, Yud-Hey, equals fifteen (which is the total of coils in the first two spaces), and the second part, Vav-Hey, equals eleven (the total for the third space). The last space then is the numerical value of "Echad" -- "One."