How does a mutual fund and cd work?

They are two very different things.

A CD is similar to a savings account in that it is in cash, low risk and you earn a set interest rate. To get this, you have to commit to locking your cash up for a certain period of time. You buy these through banks and they are typically free.

A mutual fund is a basket of stocks, usually grouped by either an index or an investment sector. By purchasing a mutual fund, you are buying a little bit of each of those stocks. Funds are a great way to diversify and reduce risk while still being invested in stocks. The best place to buy funds is through a no-load company like Vanguard or Fidelity. Other companies will charge you a fee to purchase and that is a waste of money. You should also look for funds whose expenses are under.75%/year.

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A mutual fund is a group of individual stocks, a portfolio, managed by a person, a fund manager. A CD is a certificate of deposit, much like a bank savings acct, only you must leave the money in the account for a stated period of time or there's a penalty for early withdrawal. They are both investments.

A mutual fund is a portfolio of stocks that seek a particular objective, for example long term capital appreciation, or current income. They are generally managed by a team of investment managers, and they can fluctuate in price daily. Being an investment you can lose money by investing in them, but you could potentially also achieve a higher rate of return. Most typical today, mutual funds will charge you an up front sales charge ranging from 0-no higher than 8.5%. They also usually have fees associated with them to pay the managers. Some funds will charge a fee when you take your money out of the investment, although if thats the case they cannot have an upfront charge. Given the right investor, they are one of the better forms of investing for a future objective (retirement, house, etc...)
A CD is usually an FDIC insured investment that will pay a specified interest rate given you hold the CD for the specified period of time. They do not lose value, and historically have not earned an interest that is comparable to mutual funds or stocks. These are best used to protect an investment and to keep pace with inflation over time.