The two beams (split in the beam splitter—the little rectangle with a diagonal in the center) add or subtract constructively at the output, which yields fringes that are visible to the naked eye. These fringes will move as light from one of the arms of the interferometer takes a longer or shorter path

This explanation is bit incomplete. If you align the interferometer perfectly then it should not have any fringes, the fringes indicate that there is some angle between the light beams. If you get the interferometer aligned then the beam intensity varies as function of the difference of beam path lengths.