A connector lets Claude reach into an app you already use. Until you add one, you are the courier: you copy data in and paste results out. A connector cuts out the courier, so Claude can read (pull a file from Drive, catch up on a Slack channel) and act (create a ticket, post a message) directly.
The golden rule: Claude inherits your permissions, so it can never see what you can't. Read is low-risk; enable act, or write, connectors deliberately, because they change the real world. Connectors are built on MCP.