 To transform means to change the composition or structure of something. A signal like the sound wave you are hearing as I speak is made up of air molecules compressing and expanding over time. This movement is transferred into electrical signals by tiny hairs in your ears called stereocilia. In your ear there are many groups of these stereocilia, each responding to a different frequency. The electrical signal each group generates tells your brain how much of that particular frequency is present in the signal. Your brain performs the biological equivalent of a Fourier transform, turning a time-based signal into a collection of sinusoids at different frequencies. This is what a transform does, represents the same signal out of a different set of building blocks. In the case of the Fourier transform, these building blocks are sinusoids. The Laplace transform builds a signal out of decaying sinusoids and the wavelet transform builds a signal out of wavelets.