A Green Card holder or permanent resident is entitled to live and work permanently in the U.S. It is understood that a foreign national who has received this status has complied with all requirements listed by immigration authorities.
Permanent residents can travel abroad without the risk of being denied to come back, unless it is determined that they pose a threat to national security or have violated the rules of their immigration status.
You can get a Green Card through family members, marriage, an employment-based visa, or investment.