It shows whether the agent will receive incoming chats or not. It is at the top right-hand corner of the agent's interface, on the left side of the picture. The status can be changed with its toggle. If the status is green - available - that means that the agent will receive incoming chats. If the status is red - not available - it means that the agent will not receive any incoming chats. This is how the statuses look like:
There is also an availability status circle on the picture, that changes its color in regards to the current status.