There are many physical phenomena that can be modelled by sine waves:
Waves in water are an obvious example,
Compression and rarefaction in the propagation of sound,
Transmission of all electromagnetic radiation,
Vibrations of strings in musical instruments,
Bodies "bouncing" on a spring.
Also, more complicated motion can be modelled by a superposition of many sine waves (using Fourier transforms). This enables complex motions to be studied more easily.