I've no idea what nettby is.
But ARP is how computers figure out what IP address is associated with a hardware / ethernet address, so they know what ethernet address to use for sending packets to a specific IP.
ARP poisoning means you flood the network with fake ARP packets saying your ethernet address has the gateway IP or whatever IP. So then the other devices will forward packets to your machine instead of the intended destination.
As nettby didn't use HTTPS it would then be trivial to capture / read the packets and figure out everyones' passwords. I.e. the messages would be plain text, unencrypted.
Not exactly Eli5, but hope it helps.