The paused chat indicator appears when the visitor has left the website, but did not close the chat window. In that case, except for the indicator, the agent will be able to see the message "The chatter has left the website" in the conversation field. The agent can keep sending messages to this customer and once he/she is back on the website, the messages sent will be visible and they can continue with the conversation. If the customer is back, the paused chat indicator will be gone.