Demat is simply an account that allows you to hold your shares in an electronic format. A demat account converts the physical shares into an electronic form, therefore dematerializing it. On opening a demat account, you will be given a demat account number to be able to electronically settle your trades. The workings of a demat account is very similar to that of a bank account where you keep your money with the option to deposit and withdraw.
To conduct your stock trading activities you require a trading account. This is because when a company lists its shares in the stock market you can trade the same on an electronic system through a special account known as a trading account. You can get such an account by registering with a firm or a stock broker.