The Fourier Transform works on signals of infinite duration. But if we only measure the signal for a short time, we cannot know what happened to the signal before and after we measured it. The Fourier Transform has to make an assumption about what happened to the signal before and after we measured it. The Fourier Transform assumes that any signal can be made by adding a series of sine waves of infinite duration. Sine waves are periodic signals. So the Fourier Transform works as if the data, too, were periodic for all time.
