It stands for Asian American Native Pacific Islander Serving Institution.
AAPI includes any students who self-identify as Asian American or Pacific Islander. Ethnic backgrounds under the AAPI (Asian American, Pacific Islander) umbrella may include but are not limited to Chinese, Japanese, Korean, Indian, Pakistani, Filipino, Cambodian, Vietnamese, Thai, Native Hawaiian, Fijian, Micronesian, or other Pacific Islanders.
The list of possible backgrounds was not meant to be exhaustive, as the AAPI group is very diverse and can include over 50 ethnic groups and communities.