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I think the most accurate question would be: "How does a client/host connection occur from the output of the client package, going through the internal network, leaving the modem until arriving at the host and where exactly fits the role of each of these items in this process?".
The title is simple: Gateway is the device that connects this (internal) network to the internet, network mask is the default to define Ips (255 = all IPS have the same number there). Networks of up to my mistake 254 computers usually use the mask 255.255.255.0 which allows only the last different block from one computer to another. How do you relate, well, then I’ll come up with a decent answer later if no one has explained it better. : D
– Fernando Cordeiro