How is a dark fringe formed?

Hint: The term “dark fringes” are responsible for the verification of “light is wave” and this includes under Young's Double-Slit Experiment. When two wave fronts of equal wavelength and amplitude, traveling in essentially the same direction will create an interference fringe pattern.

Complete answer:
Destructive interference causes the dark fringes to appear. If the resultant amplitude and hence the resultant intensity are both zero, interference is said to be destructive. The phase difference between the two waves must be an odd multiple of and the path difference between the two waves must be an odd multiple of $\dfrac{\lambda }{2}$ for destructive interference to occur.
When the maxima of two waves are 180 degrees out of phase, destructive interference occurs: a positive displacement of one wave is cancelled exactly by a negative displacement of the other wave. The resulting wave has zero amplitude. When the waves collide in a destructive manner, the black patches appear.
In other words, destructive interference is responsible for the dark fringes on either side of the zero-order fringe. The distance travelled by light from one slit is $\dfrac{1}{2}$ wavelengths longer than that of light from the other slit. At these points, crests and troughs meet.

Note:
Interference of light waves causes the phenomena, which is generated by superimposing trains of waves so that when their crests coincide, the light intensifies; however, when the trough and crest meet, the light is destroyed.