Meaningful human-AI collaboration requires more than processing language; it demands a deeper understanding of symbols and their socially constructed meanings. While humans naturally interpret symbols through social interaction, AI systems often miss the dynamic interpretations that emerge in conversation. Drawing on Symbolic Interactionism theory, we conducted two studies to investigate how humans and AI co-construct symbols and their meanings. Findings provide empirical insights into how humans and conversational AI agents collaboratively shape meanings during interaction. We show how participants shift their initial definitions of meaning in response to the symbols and interpretations suggested by the conversational AI agents, especially when social context is introduced. We also observe how participants project their personal and social values into these interactions, refining meanings over time. These findings reveal that shared understanding does not emerge from mere agreement but from the bi-directional exchange and reinterpretation of symbols, suggesting new paradigms for human-AI interaction design.