Brokerage Firms are companies licensed to buy and sell stocks or securities. All Brokerage Firms buy and sell stocks traded on the major exchanges, employing brokers who carry out your order to buy or sell.
Stocks represent ownership in a company. A share of stock is the same as a share of ownership. The goal is to see the value of the company increase over time and as the value of the company changes, your value in that company rises and falls.
If you have money you won't need for at least five years, and hopefully longer, then you should consider investing in the stock market. There is probably no place where long-term savings could have done better in the last 100 years. And if you want to buy stocks, you'll need a broker, or a Brokerage Firm.