Advanced Parole
If you are an immigrant in the United States and are pending adjustment of status and need to leave the country to travel abroad, then you need to get Advanced Parole to insure that you will be allowed to reenter the country upon your return. If you are pending a status change to permanent resident, temporary protective status or asylum and you leave the country, even if you just hop across the border to Mexico or Canada, you will in all likelihood lose your pending status and be denied entry back into the US. However, there is a way to prevent this.

Form I-512 Advanced Parole
The USCIS realizes that there are going to be times when an immigrant pending status has a need to return to their country of origin to take care of family or business matters. To accommodate these cases they have a document known as Advanced Parole which authorizes the departure and return to the US. You can apply for Advanced Parole using Form I-512 which can be downloaded on the USCIS website. Waiting time for these documents can run 90 to 120 days and longer around holiday seasons so you are encouraged to apply early. It's important to note that you have to have the document in your hands before you travel. Just applying for the document does not insure your reentry into the country. Also, if you travel first be aware that you cannot apply for Advanced Parole from outside of the country. If you find yourself in this position, you will have to start the whole immigration process again.

Advanced Parole for green card holders
People who have permanent resident status (green card) can leave and reenter the country at will for the most part. The green card serves as the document that allows the immigrant back into the country. However, if the green card holder is going to be outside the country for an extended period of time (over 1 year) he or she may have trouble getting back in. Depending on the circumstances for the absence, a border official may decide that you were gone long enough that your are considered as a person who has abandoned permanent resident status and the green card will be confiscated and you will not be allowed back in. One way to avoid this is to get an Advanced Parole document. If you have this document you don't even have to show your green card. The Advanced Parole document is all you need to be authorized entry into the country.

Ineligible for Advanced Parole
One last point about the Advanced Parole program. If you have been in the US illegally for more than 180 days you cannot apply for Advanced Parole. In fact you can't travel outside the United States while you are waiting to hear about your adjustment in status. Even if you file the Form I-521 and there is an error and you are issued the Advanced Parole, it will be deemed invalid if you try to use it to reenter the US.