A waveform is a graphic representation of the variations of some continuous signal with respect to time. The waveform of a sound represents the changes in air pressure (amplitude) that are caused by excitation of the air by, for example, a musical instrument.
It should be understood that this is not the only way in which a sound may be defined. A waveform represents the signal as it changes with time - it is a ’time-domain’ representation. The sound can also be represented in the ’frequency domain’; this is known as the spectrum of the sound, giving a picture of the timbre of the sound. A number of sophisticated analysis techniques have been developed, many requiring the use of a computer, which can convert (’transform’) the representation of a signal from the time domain to the frequency domain, and vice versa (the ’inverse transform’). Musicians interested in sound synthesis need to understand both representations, as they need to know the details of the spectrum of the waveforms that are being used in the synthesis process. (Source - Richard Dobson (1992). A Dictionary of Electronic and Computer Music Technology. Oxford University Press.)