All U.S. green cards—that is, the plastic identity card given to U.S. lawful permanent residents—that were issued in 1989 or later have an expiration date on the front. They are valid for ten years, at the end of which you are expected to renew your green card. The process of doing so involves submitting Form I-90, Application to Replace Permanent Resident Card, issued by U.S. Citizenship and Immigration Services (USCIS).
This is a common source of confusion, but no, your status as a lawful permanent resident will not be affected if you do not renew your green card.
However, you will face difficulty with things like proving your status as a lawful permanent resident, getting employment (which requires showing proof of your right to work in the U.S.), reentering the U.S. after foreign travel, and so forth. Besides, you are required by law to carry valid evidence of your immigration status; and an expired green card is not considered valid evidence.
The renewal requirement came as a surprise to many immigrants who received green cards between 1979 and 1988. In the past, these did not have an expiration date and did not need to be renewed. However, the system has changed, and you are now expected to renew such cards. If you haven't done so already, do so right away.
NOTE: If your green card has a two-year expiration date on it, that's a completely different matter. You are not a permanent resident, but a "conditional resident," whose actual status will in fact expire if you do not take steps to convert to permanent residence within the 90 days before your expiration date. See an attorney if that date has gone by.
You should submit your application within the six months leading up to your green card's expiration. That will give USCIS time to process the application. (USCIS is often backed up on processing; you can check its website for what's typical for your type of application in your geographic area.)
You must submit an application to renew your green card on USCIS Form I-90. Don't be confused by the fact that this form is also used for a variety of other purposes, such as to request USCIS to replace errors on a green card, or to replace a lost or stolen card.
The Form I-90 will ask you to provide such information as:
You must submit a copy of your expiring or expired green card along with Form I-90. If your name has changed since the issuance of your green card, you must submit evidence of your name change, such as a court order, marriage certificate, adoption decree.
Submit the completed Form I-90 along with the required documents and a combined fee for the application and biometrics (fingerprinting and so on) to USCIS, either online or by mail; the submission methods are described on the I-90 page of its website.
Assuming your Form I-90 is complete, the next thing that will happen is that you will receive a letter from USCIS asking you to go to the local USCIS Application Support Center (ASC) for your biometrics appointment.
After that, they will check your record, to make sure you haven't committed any crimes or otherwise become deportable from the U.S.; see Renewing Your Green Card After a Criminal Charge or Conviction for more information. This carries some risk. If the U.S. government discovers that you are deportable, you could be placed into removal proceedings and ultimately lose your U.S. residence.
USCIS might contact you for more information or (in rare cases) call you for an interview before making a final decision on your green card renewal. It will notify you about its decision in writing, and (if you're approved) send you the new card.