Modulation is a prescribed method of encoding digital (or analog) signals onto a waveform (the carrier signal). Once encoded, the original signal may be recovered by an inverse process called demodulation. Modulation is performed to adapt the signal to a different frequency range than that of the original signal. Here's how it flows:

bits -> modulator -> audio -> phone network -> audio -> demodulator -> bits

Hence the name MODEM short for modulator/demodulator. The modem is necessary because the phone network transmits audio, not data bits. The modem is for compatibility with existing equipment.