The Re-entry permit is a permit which allows you to stay outside the United States for more than 6 months, usually 2 years, without loosing your permanent residence card. You need to file the form I-131, have your biometrics taken then you can leave. It is recommended to have an attorney prepare the case if you are planning to leave. The re-entry permit will then be mailed to the attorney of record who can actually send it to you.