Can you explain about the following formulas? in Signals and System
Your question is about the Fourier series decomposition of a function (called signal here). First, this does not apply to "any signal" in theory. In practice, it applies to most pratical "periodic" signals. Periodicity is quite important, althought Fourier development may exist for not strictly periodic functions.

In loose terms, it tells you that if a signal is periodic, then inside each period the signal can be expressed as a sum (a linear superposition) of the most simple periodic functions, sines and cosines, with frequencies taken as linear factors of the base frequency.

The $a_0/2$ term comes from the average of your signal over one period $T$. This is due to the fact that sines and cosines do not see constant signals: they are orthogonal to them, since the integral of a sine or a cosine over one period exactly sums to $0$.

The other terms $a_n$ and $b_n$ are related to orthogonality as well, and i guess that you can, with great profit, read the following Wikipedia: Fourier series page in your perferred language.