A wave which is "pure" in the sense of the Fourier theorem, which states that all possible waveforms are made up of sums of component sines. As such, applying a filter to a sine wave will have no effect except to increase or decrease the amplitude, depending on the filter parameters; a filter cannot alter a sine waveform by altering the overtones because there are no overtones. As such, the sine wave is not very useful in subtractive synthesis. A sine wave is not very interesting to listen to by itself; however, in additive synthesis, sine waves are combined to make more complex waveforms. On an oscilloscope, a sine wave looks like a series of very smoothly curved alternating hills and valleys. The more commonly used basic waveforms in subtractive synthesis are the triangle wave, pulse wave, and sawtooth wave.
You may occasionally see references to a "cosine wave", particularly in regard to a quadrature oscillator. Mathematically, the cosine function is different from the sine function; however, they both produce the same waveform and they sound the same. The cosine wave is merely shifted in phase, 90 degrees relative to the sine. There are certain applications for combinations of sine and cosine waves (notably in frequency shifters), but there is not much point in an ordinary VCO producing both sine and cosine waves.
Sine waves are also used as control voltages, for example for FM synthesis, or as an LFO.