Let us take an example, a white ray (which is composed of bunch of frequency components) is passed through a prism, the ray gets split (decomposed) into its elementary vibgyor colours (i.e.different colour frequencies) and we get rainbow like pattern.
Also,We know that a Fourier series for signal $x(t)$ is given as
$$\frac {a_0} 2 + \sum \limits _{m=1} ^\infty \left(a_m \cos \frac {2 \pi m t} T + b_m \sin \frac {2 \pi m t} T \right)$$
Here, $a_0$,$a_m$ and $b_m$ terms are termed as Fourier coefficients in the Fourier series formula.
But,which information do they provide about the signal $x(t)$? Also, What is the significance of the Fourier coefficients?