Dividends are payments a company makes to its shareholders out of corporate profits. It is the income you receive for investing in the stock market.
Typically the returns derived from equity based investments like stocks take the form of capital growth (through a rising stock price) and income through dividends.
It's important to note that not all companies pay dividends. Newer companies and those experiencing high growth may decide to re-invest all of their profits back into the business. This may be a better outcome in the long term as it will grow the value of the business. But income investors want the cash now (or at least on a regular basis) rather than at some point in the future.
A convenient way of expressing this income component of return on your stock market investment is as a dividend yield. It's calculated by dividing the amount of the dividend by the price of the share. So a stock trading at $20 which pays a dividend of $1 would have yield of 5% (1 divided by 20).
But don't worry too much about the maths. These yield figures are available in the business section of most newspapers and on all of the finance and investing web sites (like Yahoo Finance and others). Using this figure, you can then compare the returns on offer for various stocks and get a rough idea of the relative values involved.
You can also compare the dividend yield to the interest rates available on the various bank savings accounts and other income investments. Just be aware the buying stock is not the same as putting money in the bank. The risks involved are much greater - you're not comparing apples with apples.