The main purpose of the new "Projects" feature in Claude.ai is to enhance collaboration and knowledge organization for Pro and Team users. It allows users to organize chats and curated knowledge sets in one place, utilize a 200K context window for adding relevant documents, ground Claude's outputs in internal knowledge, define custom instructions for each Project, and share conversation snapshots with team members. This feature aims to integrate Claude more seamlessly into existing team processes, enabling users to save time and elevate their work by leveraging Claude's capabilities within a structured, collaborative environment.