A dividend is a distribution to shareholders of retained earnings that a company has already created through its profit-making activities. Thus, a dividend is not an expense, and so it does not reduce a company's profits. Because a dividend has no impact on profits, it does not appear on the income statement. Instead, it first appears as a liability on the balance sheet, when the board of directors declares a dividend. Then, after the company pays the dividend, it still only has an impact on the balance sheet, where the amount in the retained earnings line item is reduced (as well as the amount of cash, assuming that the dividend is paid in cash).
The only way in which a dividend might reduce profits is from the perspective of future profits - paying out large dividends might starve a company of the cash that it needs to fund future growth, though only if the profits from the future growth exceed the company's cost of capital. In other cases, where a company simply has excess cash for which it cannot find a use, the distribution of that cash as dividends should not have any impact even on its future profit potential.
One area in which dividends may have a small impact on profits is that the cash could otherwise have been invested to generate interest income. Once the cash is paid out to investors, the opportunity to generate interest income is lost.
Dividends are most commonly issued by established firms that do not have to re-invest a large part of their cash flow back into their operations.