The Fast Fourier Transform is an algoritm to do a Fourier Transform.

A Fourier Transform transforms data between de time and frequency domain, which gives anoter perspective on the data.

Imagine a simple trafic light:

In the time domain, the traffic light is first Green, then Orange, then Red in a repeating cycle.

At any given moment in time, you only see a single color, so looking in the time domain doesn't tell you anything about which and how many colors exist in the sequence.

By transforming this sequence into a frequency domain (the frequency/wavelength of the light), you will see 3 distinct peaks corresponding to Green, Orange, and Red.
In the frequency domain, you can imediately tell which collors exists, but you don't have any information about the sequence in time for these colors.

FFT is used for about everything:
In sound it detects individual notes in chords.
In images, it is used to detect all colors and intensities.
In data, it is used to detect patterns.
Etc...