Almost everything in our world can be described as a wave function, and any wave function is a sum of sinusoids of different frequencies. This means that the wave function can also be represented as a set of frequencies. From this, the original wave function is able to be changed by filtering out certain unwanted frequencies or boosting a frequency. The image below shows how a single sinusoidal wave looks as a frequency. Since a function can be graphed as a bunch of sinusoidal waves, a Fourier Transform graph with peaks at the waves' frequencies can be created.
http://mri-q.com/fourier-transform-ft.html
In electronics, the original data might not be a wave function, but it can be represented as one. This wave function can then get filtered by a combination of resistors and capacitors. The order and values of these determines what type of filter it will be, and what frequencies it will filter out. This can for example take any noise out of the data, or only select a certain range of important frequencies. One will still have the same data in the original way, for example a voice file, but it will sound better due to the filtering.
• http://www.thefouriertransform.com/
• https://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/
• http://rundle.physics.ucdavis.edu/PHYGEO30/Fourier_Transforms.pdf
An extra video on what the Fourier Transform is • https://www.youtube.com/watch?v=spUNpyF58BY
For explanations on the more mathematical Fourier Series: https://www.youtube.com/watch?v=r6sGWTCMz2k&t=8s, also the videos linked at the end of this one