Do you know what a dividend is? It's the money (or stocks with a stock dividend) that a company periodically gives to its investors, the shareholders.
The the longevity and gender dividends are similar. I think the basic idea is that you need to make money (i.e. work) to spend money, and people are working longer (longevity) and more women than ever are working (gender). Both of these are caused by "investments", for example investments in better medicine so we live longer. The dividend is the benefit the economy gets when there's more money being spent as a result:
And with the increasing power of women as consumers, bringing women into decision-making roles is more important than ever to help tap this growing market. Already, women control roughly US$20 trillion of total consumer spending globally and influence up to 80 percent of buying decisions.
Acknowledging and investing in women can yield a significant return—a return known as the gender dividend.
The Gender Dividend
This article gives a more technical perspective:
This gender dividend would be reflected through increases in the support ratio—the ratio of producers to consumers in the economy—over time. When there are more working-age individuals (producers) than those who depend on them (consumers), an opportunity for increased saving and faster economic growth arises. More women in paid formal work will increase the support ratio.
Investing in Women and Girls for a Gender Dividend