What is the demand and the supply in a market ? How can you draw them how do you derive the optimal price and quantity *?

The demand is the quantity that consumers demand for a good/service at a certain price. The more quantity asked,  lower is the price. The demand has a negative slope.

The supply is the quantity of a good/service that producers are willing to sell. The more quantity, the higher is the price. The supply has a positive slope.

To find the quantity * and the price p* that are exchanged on a market, you have to pose the equation of the demand = the equation of the supply. From it you derive the numerical values of q* and p*.