This article aims to provide a theoretical account and corresponding paradigm for analysing how explainable artificial intelligence (XAI) influences people's behaviour and cognition. It uses insights from research on behaviour change. Two notable frameworks for thinking about behaviour change techniques are nudges - aimed at influencing behaviour - and boosts - aimed at fostering capability. It proposes that local and concept-based explanations are more adjacent to nudges, while global and counterfactual explanations are more adjacent to boosts. It outlines a method for measuring XAI influence and argues for the benefits of understanding it for optimal, safe and ethical human-AI collaboration.