A stock is a piece of paper (or electronic equivalent) that represents ownership in a company. An investor opens an account with a stock broker, and then buys a number of shares in a publicly traded company. Each share you own represents a certain percent ownership in a company. If a company has 1000 shares in total, and you buy 100 shares, then you own 10% of that company.
Most companies have millions of shares outstanding, even billions, and the average investor owns about a hundred shares or so, which is an extremely tiny percentage of a company.
The major goal of course is to invest in a company in which their earnings are growing. When earnings are growing fast, most often the price of that stock rises. You essentially own a small percent of a financial "pie," and it's better to buy stock in a company in which that pie is getting bigger and not smaller.
Stocks are traded, or bought and sold, on a stock market. A stock market is a place where buyers and sellers meet electronically. A buyer makes an offer for a stock at a bid price, and a seller offers to sell it at an ask price. When a buyer and seller meet at the same price, then a transaction takes place. There are usually one to three pennies difference between the bid and ask (be wary of stocks that have large gaps in the bid and ask, as the exchange may be shimming). The New York Stock Exchange is mostly a human exchange, where a specialist supervises all trades in a particular stock. The Nasdaq is an electronic exchange, where computer programs match the most similar bid and ask prices together to make trades. The Nasdaq uses human market makers in smaller capitalized stocks, who actually possess an inventory of some stocks to buy and sell, and thus the market is not completely electronic.
Useful concepts about individual stocks include dilution, float, and employee stock options. Dilution is when a company increases the number of shares outstanding, but you still own your 100 shares or so. Thus, your piece of the total financial pie got smaller. Dilution often occurs when a company buys another company and pays for it with stock, or when companies have financial problems and have to sell stock to raise cash (known as a secondary offering). Float is the number of shares that regularly trade on a stock market. A company with a small float has shares that are tightly controlled by management or large institutions. Such companies have greater volatility. Supply and demand prevails, and if there are more buyers than sellers, such a stock could go up very quickly (or down quickly if a large seller appears). Employee Stock Options are now expensed and published each quarter. There are countless companies that essentially steal from their shareholders by giving large stock awards to a small group of managers, and now this information can be evaluated before investing in any company.
Stocks are generally classified as small capitalized (cap), mid cap, large cap, and now mega-cap. In general, the smaller the capitalization, the higher the volatility and risk (although large caps can also be very volatile, due to good or bad news or market events).
Another concept is the impact of the stock market itself. There is a saying, "when the tide comes in, all the boats rise." If the market is in an up trend (bullish), then more stocks tend to go up. When the market is going down (bearish), then more stocks tend to go down. A book was written in the 1970s ("A Random Walk" I believe was the title), in which someone through darts at a newspaper stock table, and that portfolio outperformed a flat market during the next year. Individual investors must study the entire market, and the economy, before seriously investing.
Stocks can have capital gains or losses, and dividends. A capital gain or loss is when you sell a stock at a different price than what you paid for it (either at a profit or loss). Dividends are paid quarterly by many companies, as an incentive to get people to invest in their stock. Please remember, such income is usually taxable, and your accountant should advise you on making such transactions.
Most importantly, small investors should avoid putting "all their eggs in one basket," and possibly not even buy individual stocks. Mutual Funds pool individual investors money together and buy many stocks, to reduce risk. The stock market is very risky, and financial education and hiring a professional Certified Financial Planner (CFP), will increase the likelihood of making money in the stock market.