Artificial intelligence (AI) techniques have propelled biomedical sensors beyond measuring physiological markers to interpreting subjective states like stress, pain, or emotions. Despite these technological advances, user trust is not guaranteed and is inadequately addressed in extant research. This review proposes the Cognition-Context-Contrast (CCC) conceptual framework to explain the trust and acceptance of AI-enabled sensors. First, we map cognition, comprising the expectations and stereotypes that humans have about machines. Second, we integrate task context by situating sensor applications along an intellective-to-judgmental continuum and showing how demonstrability predicts tolerance for sensor uncertainty and/or errors. Third, we analyze contrast effects that arise when automated sensing displaces familiar human routines, heightening scrutiny and accelerating rejection if roll-out is abrupt. We then derive practical implications such as enhancing interpretability, tailoring data presentations to task demonstrability, and implementing transitional introduction phases. The framework offers researchers, engineers, and clinicians a structured conceptual framework for designing and implementing the next generation of AI biosensors.