Idiot version
A share is a part ownership in a company. If you own a share in SpamCo, you are a part-owner of SpamCo.

Shares can make you money in two ways.

Firstly, if SpamCo makes a profit, then the directors of SpamCo may decide to give out some of that profit to the shareholders. This is called a dividend, and usually quoted as "so much per share", so maybe SpamCo will give you 10p per share. Keep in mind that most companies have millions and millions of shares, so even if they make huge profits, the returns per share can be quite small. However, some companies make good, constant, if not high profits over time, so people who need a fairly constant income, like pension funds, like these sorts of shares.

Secondly, you can sell the share on to someone else, hopefully for more than you paid for it. The price of shares is always changing as people try to guess how much profit the company will make, and so how much they are likely to pay out in dividends.

General tips:

Buy shares you plan to keep - find a good company that pays out regular dividends over time, and keep it. Unless you are really dedicated, this will make you more money than just buying and selling.

Diversify - don't put all your cash into one share, or one industry. Balance things out so that if one goes tits up, the rest will be safe.

Go see your bank - a "shares ISA", which any bank will be delighted to set up for you, is not only a decent way to spread the risk around, it is also tax free. If you buy the shares directly, you pay tax on the dividends and any profit from sales.
(ragged, Mon 29 Jun 2009, 16:39, Reply)