Yes, if you have permanent resident status and therefore have a green card, you are still permitted to travel outside of the United States. When this is a brief or temporary trip, it should not affect your status at all.
For example, perhaps you moved to the United States years ago on a student visa, got a job after graduation, and obtained permanent resident status so that you could stay and start a new life in the U.S. But you still have family members in your home country. If you want to return home to visit them over the holidays or for something of this nature, you are fully permitted to do so, and you will not lose your permanent resident status just for being out of the country.
When complications may arise
There are two main issues with traveling outside of the U.S. to keep in mind. The first is if the U.S. government determines that you never had any intention of living in the country permanently. They may determine that you have abandoned your status, which could cause you to lose your green card. But a simple trip home to see your family is not going to give them this impression.
It is a bigger issue when you travel for an extended period of time. Generally speaking, if you are going to be outside of the U.S. for more than a year, then you may need to take additional steps.
For example, you can use Form I-131 to apply for a reentry permit. If you do this before your trip, knowing in advance that you are going to have to leave for more than a year, the permit can allow you to reenter. It also helps establish that you do intend to live in the United States, even if you feel obligated to take an extended absence.
Understanding the complexities of the situation is important to your immigration status, so be sure you know exactly what legal options you have.
