AFP stands for Administradora de Fondos de Pensiones and refers to one of several private companies in charge of managing the mandatory and voluntary retirement investments of the majority of Chile’s workers. (Some still have their retirement funds with the INP, the pre-privatization government entity that was charged with the same task.)
When you first become an employee in Chile you will be required to choose an AFP to receive your salary retirement withholding. You will need to instruct your AFP to allocate your contributions to one or more retirement funds. Each AFP has 5 funds, A to E; A funds have the highest risk and E the lowest. If you don’t make the choice, they will allocate all of your contributions to one fund depending on your age.
The percentage of your gross salary you contribute to your AFP is not standard but rather varies slightly among AFPs; you may want to consider this when choosing one. This is also important to keep in mind when calculating withholding for domestic employees (link). You can compare the AFPs’ fee structures here.
As a foreigner, you can liquidate your retirement account (at any time, as far as I know). Contact your AFP for details. If your home country has a social security reciprocity agreement with Chile (as the U.S. does), it may make the most financial sense to leave your AFP account intact. An accountant can help you decide.
The Superintendencia de Pensiones is the governmental oversight body and has a useful web site. See Information for workers and retirees including an AFP comparison tool.