In this paper, we examine the meaning of conversing with pedagogical agents. Previous research has focused on examining cause and effect relationships, failing to take into account the meaning of the experiences individuals have when holding a dialogue with conversational agents for educational purposes. To understand these experiences, we have conducted a phenomenological examination of what it means to converse with a pedagogical agent. In phenomenological terms, findings suggest the experience is complex, engrossing, virtual yet real, human-like, and social. Implications for the future design, implementation, and research of conversational agents in educational and other settings are discussed.