If 1, my thoughts are same as yours.
If 0, you may agree after reading this blog.
Damping is any effect that tends to reduce the amplitude of Simple Harmonic Motion or any oscillation.
Take a sinusoid (which is a smooth repetitive oscillation) for instance (this can also be thought of as cosine, with a phase difference), the waveform looks like this:

The same waveform, when damped looks like this:

According to Fourier series, complicated periodic functions are written as the sum of simple waves mathematically represented by sines and cosines.
So, almost all the signals in the nature can be approximated to Fourier series.
How is damping saving our lives?
A natural signal, speech. When any person speaks, the speech (which can be represented by Fourier Series) damps after some time. This can be seen from the following speech wave form:

This is the same reason,
- why we cannot hear a person speaking at some long distance.
- why when a word is uttered, we could hear the word.

