Although there's no general legal definition for the term "mutual fund," a mutual fund generally refers to an investment fund that is professionally managed and pools together money from many investors with each investor owning a share of that investment fund. However, let's go a bit further...
We won't go into the laws of mutual funds - almost every country has its own laws on how a mutual fund can be set up and managed. Briefly, mutual funds are usually regulated well and have certain tax advantages if they comply with certain requirements.
The more important thing about mutual funds for retail investors, however, is their general structure. A mutual fund is actually a very amazing financial creation that allows investors to purchase shares in a large amount of companies (allowing them to diversify their holdings) very easily with little effort and little cost relative to replicating the mutual fund's portfolio with individual securities.
A mutual fund basically is a company that buys a bunch of shares of different companies (or bonds) and then packages them all together. Then, it sells shares of that new package. So, when you buy a share of a mutual fund, you actually buy a small piece of each of the shares of the individual stocks that the mutual fund is made up of.
Mutual funds usually have specific tilts or styles - some mutual funds focus on US equities while others focus on international equities while others focus on oil while others focus on real estate while others focus on bonds and so on and so on. There are a plethora of mutual funds to choose from and you should easily be able to find a fund that matches your investing strategy. There are even target date mutual funds that are specifically designed for people planning to retire in certain years - these funds become more conservative as the target retirement date fund approaches.
Fees are important for mutual funds - mutual funds charge a fee for the services they provide. Fees are very important - be mindful not to pay too much in fees because paying high fees will deeply eat away at your earnings over the long term. A popular firm that specializes in low-fee mutual funds (and the one that pretty much started the low-fee mutual fund sector) is Vanguard. Their average fee (according to their own website) is 0.18% while the average mutual fund fee in the industry is 1.02% (also according to Vanguard's website). Be mindful when choosing a mutual fund - you don't want your earnings to be consistently eaten away by high fees.
Finally, there are generally 2 types of mutual funds:
P.S. For more on how detrimental high fees can be to your long-term returns, check out this bulletin produced by the SEC