There are different states in which your worker can be in regard to mining and responsiveness.
Online: Worker is online when the minerstat software and mining client are running and the hashrate is larger than 0 H/s (worker is mining).
Inactive: Worker is inactive when the minerstat software and mining client are running, but mining client reports 0 H/s (worker is trying to mine, but there is an error which is interrupting it).
Idle: Worker is idle when the minerstat software is running, while mining client isn't running (the worker is not mining). The idle state is normal in the first few seconds when you have just booted your rig.
Offline: Worker is offline when the minerstat software isn't responding. This state is also called unresponsive in triggers. Offline state happens when the rig is shut down, in the first few seconds of boot, if there is no internet connection, or if minerstat software isn't properly running on the rig (even if the mining client is running).