A margin call is issued by a broker to require a customer with a margin account to bring the funds in the account up to a minimum required amount to keep the brokerage safe from too large a loss.
Margin is the use of borrowed funds (borrowed from the broker) to invest in equities. This is leverage and can result in both great gains and horrible losses. A margin call is more toward the loss side than the gain side.
In allowing you to borrow money, the broker sets certain limits on how much the assets in your account must be worth. Those assets (e.g. the stocks in the account) are the collateral for the loan the broker is making to you. If the value drops below that limit, then the broker requires you to pay back enough of the margin (borrowed funds) to bring the value back up to that limit. This is a margin call. You must either deposit more cash into the account or sell parts or all of your holdings to generate enough cash to cover the margin call.
Danger, Will Robinson!
Of course, the reason the margin call happens is usually because the value of your holdings has declined, so the sale of those holdings usually comes at the worst possible time, after they've dropped in price. Oh, well. All the broker cares about is getting its borrowed money back. You must satisfy the call or the broker will sell the assets for you, without regard to the value or which individual ones, in order to recover its money.
To reiterate because this is a really important point: Be aware that notification of the margin call is a courtesy and not a requirement. Your broker can sell your securities without notifying you, getting your permission, or giving you time to put more money into your account.
Your brokerage will set the maintenance amount that must remain in your account, as a percentage of the total value of your securities. Since markets are volatile -- and the value of your investments could drop or rise significantly in a short period of time -- the maintenance amount could also drop or rise significantly in a short period of time.
Just because you're rich...
Owning a company or having a lot of money doesn't make you smart. There are several examples of people having to sell nearly everything to satisfy a margin call. One such is Aubrey McClendon, co-founder of Chesapeake Energy. It turns out that he was so confident in the future of his company that he borrowed heavily to buy even more shares of his company. When the stock price declined sharply in the latter half of 2008, he faced margin calls and ended up selling almost his entire position to satisfy them. 
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- Fool.com: Fool FAQ - Margin
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