Firstly, it should be clear that the black stripes on the tallit and/or tzitzit are not mandatory. Many have other colors on their tallits, and many have completely white ones. Nevertheless, it is traditional in many communities to wear a tallit and tzitzit which sport black stripes.

Some suggest that the stripes are to remind us of the blue techelet.1 Indeed, some communities have the custom of using (dark) blue stripes, not black. For those whose custom it is to use black stripes, perhaps this is so that one should not erroneously believe that real techelet was used. (Because if we would have techailet we would use it to dye the tzitzit strings with it, not the garment).

Also, the Zohar2 explains that white represents chesed (Divine Benevolence) and the blue (black, dark) stripe represents gevurah (G‑d's severity).

Furthermore, the mitzvah of reciting the morning Shema begins when it is light enough for one to distinguish between white and techelet.3 Since we no longer have the techelet, the black stripe in the cloth of the tallit can be used to ascertain whether the time for reading the Shema has yet arrived.