Beta Meaning


What does beta exactly mean?
As far I understand, beta tells us about the company return if it s more or less volatile in comparison with the market return

Please correct me if I am wrong

Not quite.

In addition to relative volatility of returns, there’s the correlation of returns:

\beta_{stock} = \rho_{returns_{stock}, returns_{market}}\left(\dfrac{\sigma_{returns_{stock}}}{\sigma_{returns_{market}}}\right)

Therefore, beta can be less than 1 even if the returns of the stock are more volatile than the returns of the market.