In mathematics, a sine wave is a continuous, smooth wave. It is used to mathematically model waves in the real world.
Look at the image from Wikipedia showing several drill bits. Can you see how the bottom drill bit is composed of 4 separate sine waves?
Sine Curve and the Unit Circle (Stationary Circle) (0:55)
Sine Curve and the Unit Circle (0:26)
It is possible to build any real-life sound from a combination of sine waves.
Additive synthesis: building sounds with sine waves (5:42)
Sine Wave to Square Wave using Fourier Series (1:03)
Wikipedia has an animation demonstrating how a perfect square wave (blue dot) is approximated using the sum (purple dot) of six sine waves.
In university, you may learn about how sine waves can be thought of as circular waves with a real axis and an imaginary axis.
Complex Sine Wave (0:59)