what does this exactly mean if a device (projector,tv, etc.) has the 'AMX DEVICE DISCOVER" option available on the menu ?
This will enable a device beacon that will broadcast udp on the network. The Netlinx master, if programmed with a matching module would then attempt to establish a connection for device control.
A quick example would be that you are anticipating a Lutron Lighting control system to be on the same network, but you do not know it's network address at the point of commissioning. You have configured the program to be listening for it and after hearing the device announcement on the network, the two systems connect the dots and you are controlling the end device.
More info here https://trade.amx.com/assets/whitePapers/AMX.Dynamic.Device.Discovery.White.Paper.pdf
Specifically Section 4. Run-time Dynamic Device Discovery as to how it used in practice with regards to binding Duet modules to a port based on the device identified in the beacon.