An order is nothing but an instruction that an investor gives to buy or sell stocks on a trading platform or to a stock broker. There are different order types in the market.
A brokerage house (firm) is simply a place where investors and traders go for buying and selling stocks. The broker house acts as a middleman between buyers and sellers, and provides a trading platform for everyone. It charges commission on these transactions. Every time an investor buys a stock, a transaction fee is charged.