Dividends are payments by the company to shareholders. If the company has some extra cash hanging around, the board can give some of that cash back to investors in the form of a dividend. Sophisticated investors are not investing in your startup to get dividends, so dividends should not be a major sticking point in a term sheet. The company should attempt to only give dividends if and when the company's board of directors decides to grant them, and can make a strong case for this since investors aren't investing for the dividend in the first place.
Here are there are a few things to watch out for:
Cumulative Dividends: Most dividends get paid out only if the board chooses to do so - i.e., if the company is feeling generous. Cumulative dividends are required to be paid out, whether or not the company can afford it. Having a cumulative dividend-unless it's a very special case-usually doesn't make any sense. It's basically a way to sneak in an increase in the liquidation preference, because investors know the company is not going to be able to pay the dividend until it gets a liquidation event. And, do you really want to tell your next investors that you're going to be using their funds to pay dividends to the old investors? Cumulative dividends should be avoided if possible.
Payment in Kind: Payment in kind or "PIK" dividends are even nastier. They're typically combined with cumulative dividends, and state that the required dividends will be paid out in company stock. So, instead of giving the investors a certain amount of cash every year, the company is obligated to give them a larger and larger equity stake, without them putting in any more money. Even VCs admit that cumulative PIK dividends are a dirty trick. If you see them in a term sheet, run.