What are dividends and should every mutual fund offer them?

mutual funds are required by law to distribute all of their income and realized capital gains to investors. They have no other choice. So if the mutual fund has received dividends from their investments and sold securities in which they had more capital gains than losses, they will distribute them by year end to the investors.

Dividends are payments made by a company to its shareholders. When a company earns a profit, some of it is reinvested in the business and called retained earnings, and some of it can be paid to its shareholders as a dividend.
it is declared in every agm i.e annual general meeting

The definition for a Mutual Fund (MF) from Wikipedia:
A mutual fund is a form of collective investment that pools money from many investors and invests the money in stocks, bonds, short-term money market instruments, and/or other securities. In a mutual fund, the fund manager trades the fund's underlying securities, realizing capital gains or loss, and collects the dividend or interest income. The investment proceeds are then passed along to the individual investors.

Simply said, the net income (i.e. gross income less taxes and service charges etc) made by a fund and which is distributed to the fundholders are dividends.
And it is not necessary that every mutual fund should offer dividends. The fund managers can decide to reinvest the income back into the fund and plan for better dividends later. And there are mutual funds that do not require dividend payments to be made, especially when capital returns with fixed interest are guaranteed.