Ping sends out a signal to a target, who can be another user or even yourself. The ping response time will be in seconds and will appear in the status window. The Ping Pong you see is the result of your server interrogating you to see if you are still on the system. If you remain idle too long, you will be dropped off line by the server, which is called a Ping Timeout. But you had better type something somewhere so that the server won't drop you.
Some servers are more forgiving of idle time than others.
Those are Channel Mode Settings. Channel modes are settings that only the channel operators have access to. They are a subset of modes called Operator Modes. Operator Modes allow the operators to have a great deal of control over the channel and the users that are on the channel. Click here for a complete listing and description of all the Channel and Operator Modes.