What does this error really mean?

    error.ininedgecontrol.session.inactive - This is a benign error that happens when the agent hangs up after the caller. 

The agents are saying that the call disconnects within 3 seconds or 5 seconds before they can pick up or something like that. But, here it says the agent hangs up after the caller,.,after the caller disconnects or what happens?

Hello John,

The short answer is that that is not really an error where something went wrong, such as a call being dropped. If you see that, you should be able to ignore it. I've talked to a few subject matter experts in the past and the exact details on what triggers that 'error' tend to happen after the agent leg attempts to disconnect from a call after the remote end has already begun the process of tearing down the call. 

From https://help.mypurecloud.com/articles/disconnect-reasons/:

Client – Session is inactive         A voice provider error caused when a user attempts to work with a call that has already been disconnected.