"Green card" is the slang term for the identity card showing that a person has permanent residence in the United States. It is, in fact, green, though it has gone through many color changes over the years. The official term used for the green card by U.S. Citizenship and Immigration Services (USCIS) is an I-551 or Permanent Resident Card (PRC).
Every year, the United States government grants green cards to thousands of immigrants who meet certain strict eligibility characteristics. For example, many people obtain green cards based on:
You won't be handed a card the minute you are approved for permanent residence. Immigrants who come from overseas enter the U.S. with an immigrant visa, and are then given a temporary I-551 stamp in their passport. For immigrants who adjust status in the U.S., they will be given a letter of approval. In both cases, the actual green card will be sent by mail, some weeks later.
A green card gives its holder the legal right to live and work in the U.S. on a permanent basis. You can apply for many government jobs with a green card (though some are reserved for citizens). Green card holders also receive certain health, education, and other benefits.
You can also petition for your spouse and unmarried children to receive their own green cards, though they will be classified as "preference relatives," and due to annual limits on such visas, have to wait in line until a visa is available.
You may keep your present citizenship in your native country, and you may apply for U.S. citizenship at a later time. That time period is five years for most green card holders, but three years for people who were married to and living with a U.S. citizen the entire time.
Having a green card is not an entirely secure status, however. A green card holder can lose status if, for example, the person commits a crime or violates a law, willfully fails to advise USCIS of changes of address, or does something else that makes the person deportable under Section 237 of the Immigration and Nationality Act (I.N.A.). In addition, if a green card holder leaves the United States and tries to return, the person becomes subject to the even broader grounds of inadmissibility found in Section 212 of the I.N.A.
Green cards used to be issued with no expiration date, but now USCIS wants you to apply for a new card every ten years. Don't worry, this doesn't mean that your permanent residence itself expires -- just the card that proves it. Then again, if you fail to renew the green card, you risk running into trouble with USCIS if it discovers that you have violated the law requiring you to carry an unexpired green card with you at all times.
Don't confuse the ten-year green card expiration date with the two-year expiration date put on green cards held by conditional residents (people who got their status due to investment or a recent marriage to a U.S. citizen). The expiration of that card really does mean the expiration of one's legal status in the United States. Conditional residents must, within 90 days before the expiration date, file Form I-751 (marriage-based cases) or I-829 (investment-based cases) in order to convert to permanent resident status.