Preference shares, typically have preferred rights over other shares in the company. One of those rights can be the right to receive dividends ahead of other shareholders on a cumulative or non-cumulative basis.
If the preference shares are said to be cumulative (which is the default position), it means that dividends payable on such shares accumulate until they are paid. For example, if a dividend is payable on a certain date but the company is not in a position to pay it (normally because it has insufficient distributable reserves), the shareholder is still entitled to that dividend in preference to other dividends paid by the company.
By contrast, if the preference share is expressly stated to be non-cumulative, in the event that the company is unable to pay the dividend due on the payment date, the preference shareholder loses the right to receive that particular dividend payment.
The issue of preference shares is regulated by company law (in particular the Companies Act 2006), the Articles of Association of a company and any shareholders agreement entered into by the relevant shareholders.