The waveform of a signal is a graph of its instantaneous voltages versus time. In audio, for example, we are always dealing with periodic waveforms that make up what we hear. These periodic waveforms can be plotted on a graph and will show up as some type of squiggly (how’s that for a word?) line. From left to right is time (usually a very short slice of time) and from top to bottom is the amplitude of the sound (or relative voltage) at those instants in time. The familiar sine wave is an example of this.
Waveforms, or Waves (a Wave File, for example) are also the names sometimes given to samples or snippets of sound that are used in various electronic sound generating or playing instruments. The usage of the word comes from the definition above and has become commonplace in the modern day era of audio production where one is often looking at waveforms on a computer screen while editing sounds.