Large language models (LLMs) are increasingly used as conversational partners for learning, yet the interactional dynamics supporting users' learning and engagement are understudied. We analyze the linguistic and interactional features from both LLM and participant chats across 397 human-LLM conversations about socio-political issues to identify the mechanisms and conditions under which LLM explanations shape changes in political knowledge and confidence. Mediation analyses reveal that LLM explanatory richness partially supports confidence by fostering users' reflective insight, whereas its effect on knowledge gain operates entirely through users' cognitive engagement. Moderation analyses show that these effects are highly conditional and vary by political efficacy. Confidence gains depend on how high-efficacy users experience and resolve uncertainty. Knowledge gains depend on high-efficacy users' ability to leverage extended interaction, with longer conversations benefiting primarily reflective users. In summary, we find that learning from LLMs is an interactional achievement, not a uniform outcome of better explanations. The findings underscore the importance of aligning LLM explanatory behavior with users' engagement states to support effective learning in designing Human-AI interactive systems.