I ask this question, as someone has recently asked me this and I'm not sure I gave them a satisfactory/correct answer.
I explained that in QFT we describe particles (and there interactions) in terms of fields, which fundamentally have a wave-like nature (indeed, solving the appropriate equations of motion gives rise to exponential solutions, suggesting such a decomposition into Fourier modes). In general, we wish to describe discrete excitations in these fields and this requires us to know hoe the field is "constructed". This can be achieved through expressing the field in terms of its Fourier transform, i.e. an infinite sum of the frequencies that constitute it and the excitation modes (amplitudes) associated with each of those frequencies.
Would this description be correct at all? Any corrections, improvements and/or explanations will be much appreciated.