This feature is unique among IoT messaging protocols. The Last Will Testament or short LWT lets a client provide a testament along with its credentials when connecting to the broker. If the client disconnects ungracefully at some point later (maybe because his power source died), it can let the broker deliver a message to other clients. (Comparable to a real testament that gets communicated to the bereaved). This LWT message has the same form as an ordinary message and gets routed via the same mechanics.
Such a simple LWT mechanism can become very handy if your application has to track some sort of presence status of the participating devices.