Just as you have to open an account with a bank if you want to save your money, make cheque payments etc, Nowadays, you need to open a demat account if you want to buy or sell stocks. So it is just like a bank account where actual money is replaced by shares. You have to approach the DPs to open your demat account. Let's say your portfolio of shares looks like this: 150 of Infosys, 50 of Wipro, 200 of HLL and 100 of ACC. All these will show in your demat account. So you don't have to possess any physical certificates showing that you own these shares. They are all held electronically in your account. As you buy and sell the shares, they are adjusted in your account. Just like a bank passbook or statement, the DP will provide you with periodic statements of holdings and transactions.

Why Demat Account ?

Nowadays, practically all trades have to be settled in dematerialised form. Although the market regulator, the Securities and Exchange Board of India (SEBI), has allowed trades of up to 500 shares to be settled in physical form, nobody wants physical shares any more.
So a demat account is a must for trading and investing. Most banks are also DP participants, as are many brokers. You can choose your very own DP. To get a list, visit the NSDL and CDSL websites and see who the registered DPs are.