Mutual funds are a form of collective investment scheme that is managed by investment professionals in behalf of a group of investors. There can be many investors involved all investing small or large amounts of money that the fund managers will pool together to invest in stocks, shares, funds and commodities. These mutual funds must be managed within the rules set out by their specific financial regulators and usually have a board of directors or trustees to ensure the funds is correctly managed in the interest of the investors.
Once a fund is setup and registered with the financial authorities it can issue shares to prospective investors for cash investments. With this cash the funds manager will purchase stocks or other securities that will become the assets of the fund. The investor now owns a share of the fund and its assets.
Open-end funds are traded at the end of the day. New shares can be bought at the days closing value or old shares can be sold back to the fund for cash.
ETFs or Exchange Traded Funds are funds that can be traded like ordinary stocks on a stock exchange with the price moving continually. These shares are traded between investors hence the fund does not have to buy back the shares upon request. This allows this type of fund to require less liquidity to repay investors and hence can have lower ongoing costs.
Mutual funds can be index funds or actively managed funds. That is they can follow a given index such as SP500 or the stocks can be hand picked by the funds manager in order to try to out perform the index. Just which is best is the subject of a lot of controversy with experts being poles apart. Indexed funds do seem to have history on their side in general terms.
Buying and selling of normal Mutual funds (i.e. not ETFs) can be done directly with the fund managers where a load or fee should not be required. Alternatively you can buy or sell through a broker or financial advisor where a load or fee will be payable.