As a general rule, any person who is not a U.S. citizen or non-citizen U.S national is subject to immigration review and inspection by an immigration official each time the person seeks admission to United States. If after such review you are determined to be inadmissible (even though you have a green card or was admissible before), you may be denied admission.
Travel outside of the United States may have severe consequences if you have a pending immigration petition and did not apply for re-entry permit (advance parole) prior to travel; you may be considered to abandon that application. If you are applying for a green card based on your relationship to a U.S citizen it is really tempting to travel to your home country after you file your initial petition. I-131 application for advance parole may be a good solution for you, but you need to keep in mind that admission to United States is not a guarantee even if the appropriate documents are obtained. In all cases you are still subject to immigration inspection and examination at a port of entry to determine whether you are admissible into the country and whether you are eligible for the status sought.
In the event that you accrued certain periods of unlawful presence in the United States you may be barred from admission for either 3 or 10 years depending on the amount of time you were in U.S. illegally. Any departure from the U.S may trigger this specific ground of inadmissibility, even if you obtained an advance parole document before traveling outside of the country.
Without the Advance Parole your Permanent Resident application will not be considered abandoned after foreign travel only if you have a valid non-immigrant visa status like H, L, K or V that would allow; you to be eligible and admissible to return to the United States.
Please keep in mind that Department of Homeland Security may revoke or terminate your advance parole at any time even when you are outside of the U.S. In that instance unless you have a valid visa you will not be allowed to re-enter.
DACA recipients need to remember that their status alone is not sufficient to allow foreign travel and does not guarantee admission back to the U.S. Advance parole needs to be obtained before such travel and careful determination of the actual need to travel as the advance parole does not guarantee re-entry to the U.S. The Custom and Border Protection officer may find you inadmissible for health or security reasons for example.
Every person planning a trip outside of the United States while waiting for their immigration petition to be adjudicated should carefully determine the risks and benefits of such travel as the Advance Parole is not a guarantee of a safe return to the United States.