If you invest in a mutual fund then the fund can either follow a dividend reinvestment plan (known as an "accumulation fund") where the income from the underlying securities in the fund is re-invested or it can follow a dividend payment plan ("income fund") where some or all of the underlying income is paid to the mutual fund holders in cash. The latter of these would be classified as a dividend mutual fund.
The dividend paid to mutual fund holders can be "covered" or not. If it is covered then there is sufficient dividend income from the underlying securities to fund the dividend payments to the mutual fund holders. If it is not covered then the income can come from capital or from reserves. This means the fund manager has to sell securities to pay you or dip into the cash reserves. Most managers of dividend mutual funds are likely to target underlying investments that will pay sufficient income to fund the dividend distributions for the mutual fund.
To know whether the mutual fund you are looking at will pay dividends, you need to look at the stated objectives of the fund. This is usually clearly laid out by the managers and will state whether they will look to pay out income from the fund. Like stocks, the mutual fund will have an historic dividend yield which will give you an indication of what sort of return you will get from your original investment. Of course the future income you receive will depend on the underlying performance of the investments and the pay outs the fund manager decides to make.
Whether you invest in dividend mutual funds depends on your situation. If you are relying on consistent income from your portfolio, for example if you're retired, then dividend mutual funds can be a very good option. They will take away the hassle of monitoring your investments, give you diversity and you have a professional looking after your money. Do remember, though, that you may have to pay tax on these payments which will be taxed at your income tax rate unless the dividend is considered a qualified dividend which will give you a lower rate.
An alternative to mutual funds could be exchange traded funds (ETFs) which try to track certain indexes or sectors. They also potentially give you the advantage of diversity but many ETFs have lower fees than mutual funds and mean you don't need to worry about the quality of the manager you have picked. Many ETFs payout dividends as well.