A default gateway is only a small part of that higher topic of IP networking and, as an application engineer for many years, the best way I can describe this is by using the concept of the post office as I have done so many times before.
Every device that exists on a network or the internet has a unique address known as a TCP/IP address of the format ###.###.###.###. Think of this in the post office analogy as a street address. Attached to this address is the Subnet Mask which also has the format ###.###.###.### except that its numbers usually are either 255 or 0. Sometimes they vary but we won't get into that because it'll confuse things. This mask is used to tell a computer how deep into the address it is allowed to search to find a location.
So, as an example, if I had an address of 192.168.0.123 and a subnet mask of 255.255.2555.0, I would be able to find adresses within the range 192.168.0.0 and 192.168.0.255 or thereabouts. Effectively, as a postal worker I can only deliver to 255 addresses. If I change the subnet to 255.255.0.0 then my territory expands to 192.168.0.0 to 192.168.255.255 so I get many more addresses that are available to me for delivery.
But what if I'm asked to deliver data to an address that lies outside of the maximum subnet of 0.0.0.0? What then? That is where the DEFAULT GATEWAY comes in because the DEFAULT GATEWAY is the address of the server or servers that contains either directions to the address that I'm looking for or it knows another server that does know.
It is in this way that data is able to leapfrog from server to server until its packet of data gets delivered to its ultimate destination.
So remember, when trying to figure out networking...just think of the Postal Service and how they get their mail from Point A to Point B. It's the same idea.
Learn more about this author, Robert Elliott.
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