Well yeah, context usually provides clarification and understanding of the "thing". I suppose that might extend to why the "thing" is important, but that might be somewhat subjective.
I remember a similar situation when I was studying calculus, I asked, "What's with all these integrals, derivatives and limits, when will we ever use this again?" Some of the questions were then put in context and it changed my view of calculus forever! Suddenly all this dry and boring math became fascinating as we were calculating the trajectories of bullets and cannonballs, the escape velocity of rockets and many other real world examples.
Disclaimer: The following is not intended to be taken personally.
I just assumed, perhaps wrongly, that an EE student would have had enough interest in electronics to already be familiar with the concepts of time domain and frequency domain having probably used an oscilloscope and at least seen a spectrum analyzer. I would have expected much more excitement about learning that there was a mathematical method for transforming a signal back and forth between the two domains. The implications of this are fundamental to DSP (Digital Signal Processing). FFTs are used everywhere these days, you probably have more than one app on your phone that uses an FFT, such as that app that can sample a few seconds of a song and then tell you what song it is. When I was younger FFTs were only just becoming fashionable with the emergence of DSP processors.
According to this site only one person has followed the link I posted above. The videos are quite short but demonstrate the elegant simplicity of the Fourier transform, that is they provide context.
PS. Oh, and no, I was not a ham.