Discount Broker is a financial organization that places trades at a discount to a full service broker, and also often will serve as a custodian for assets. With the onset of online trading platforms, the discount brokerage industry has seen plenty of growth over the last few years.
In many cases, however, a discount broker will not offer any investment advice - hence the discounted price for trading services. An investor that wants a lot of personalized service should probably consider a full service broker over a discount broker, since a discount broker literally only focuses on trade execution and will not provide additional services, like research and advice.
Examples of discount brokerage firms are TD Ameritrade, eTrade, and even Schwab has a discount brokerage window.