Proprietary ('prop') trading involves banks risking their own capital to make money.
Banks usually trade shares for one of three reasons. First, they may be acting as a broker to a client an institution such as a pension fund or an individual. Or the bank may be acting as a market maker buying and selling securities to fulfil its obligation to an exchange in order to allow other investors to trade.
However, proprietary trading involves banks risking their own capital to make money. They may trade equities, but also bonds, currencies or commodities. Prop trading is pure speculation and can trigger big profits or losses. For that reason critics argue that it should be split away from much safer activities, such as accepting deposits and making loans, if banks are to retain the right to future taxpayer-funded bail-outs.