A stock is a share or a piece of a company. Each share represents a percentage of ownership within a company. The stock market is a place for the sale or purchase of various companies stocks.
The stock exchanges act as an intermediary between the company and the trader, or a trader and another trader.
The biggest difference between trading and investing is the motivation. When investing, someone is looking to hold a stock for a long period of time and to build wealth over that time. Investing typically comes with much less risk than trading and is viewed as a long term strategy. Trading on the other hand, is for people looking to turn a profit quickly. There is typically much more risk involved with trading (whether it be day trading or a longer term swing trade). Trading is a shorter term holding of a position than investing-sometimes for as little as only a few seconds.