Stock Market is a trading platform were Buyers & Sellers trades the shares, its called as Secondary market. The company who issues shares for the first to the Public is called Primary market & its been through IPO(Initial Public Offering).
A share holder is called as Part Owner of the company and has rights to sell its shares, eligible for Bonus, Dividend.
NSE & BSE are the exchanges been monitor by SEBI; were retail investors can buy & sell the shares.