The notion of "independence'' is frequently used to motivate technology design in the HCI sub-field of accessible and assistive technology for people with disabilities. Despite the term's pervasive use, the literature lacks a recent articulation of its meaning in the context of assistive technology. What does independence really mean? Scoping the study to people with visual impairments (PVI), we posed this question to 10 individuals from diverse backgrounds through in-depth, semi-structured interviews. Our findings reveal that PVI have internal experiences of independence and social experiences of independence, with surprising insights into the roles that people and technology play in supporting independence. We also discuss new ways to design for independence.