Could somebody describe to me what these are in relations to acoustics?

Take 2 pure tones of different frequencies. Sometimes they will be in phase, and the amplitude of the combination is high (reinforcement), and sometimes opposite in phase, and the amplitude is low (cancellation). The two frequencies combined generate a new frequency equal to the difference between them (beat frequency). There are conventionally 3 basic wave shapes (sine, square and triangular), but I suppose you can divide triangular into symmetrical and ramp. The addition of harmonics to a tone give richness to the sound (and produce complex waveforms). The proportions of harmonics help to distinguish a piano from a guitar or violin.