A Cumulative Dividend calls for some amount of money (usually a percentage of the original price paid per share of the preferred stock) to accrue for each share of preferred stock, whether or not the company ever declares that dividend. Because, on a liquidation event (e.g. sale of the company), the preferred stock is typically due its Liquidation Preference AND any unpaid dividends, Cumulative Dividends effectively increase the Liquidation Preference over time. Cumulative Dividends are similar to the effect of interest on debt. For example, if an investor invested $1,000,000 with Cumulative Dividends of 10% per annum, then the Liquidation Preference would grow by $100,000 every year (unless the dividend was paid out by the company at an earlier time). Note that the Cumulative Dividends do not compound.
These are dividends payable on stock that are only paid if and when they are declared by the Board of Directors of the company.