@dmurph3, your router issues IP numbers (the four-position numbers) to all devices in the network. Your Mac got the number 192.168.1.3, while the router itself has 192.168.1.1. Every device, as I said, has to have a unique number so that data to and from that device can be managed properly. When you entered 8.8.4.4 and 8.8.8.8 into the DNS list, you are telling your computer that in addition to looking at 192.168.1.1 to resolve names, it should also use those two addresses, which happen to be the Google DNS Server worldwide.
More detail: Every device in the entire world has to have a unique identifier in the network. EVERY. DEVICE. In the early days when the system was originally being designed, it was thought that a string of four numbers would do, in the form of w.x.y.z, where w, x, y and z were in the range of 0-255. That arrangement provides for 4,294,967,296 unique devices in a 32-bit address stream. But it was realized pretty quickly that the number of devices was likely to grow far beyond that. Today there are an estimated 20 billion or more devices in the internet. So how do we identify 20+ billion devices with only 4 billion addresses? The solution was called "sub-net." Certain ranges of numbers were reserved for local area networks, small nets attached to the larger internet through various service providers. 192.168.1.x was one of those subnets. It was reserved for networks with up to 256 devices. The way it works is that the modem/router that actually attaches to the Internet Service Provider (where you subscribe to access), or ISP, establishes an internal network in your home that uses that subnet for locally attached devices. For most of us 256 is plenty for now. I have currently 23 devices, for example, in my network. With smart connected TV, phones, computers, smart speakers, Alexa-type devices, etc., all expanding, 256 may be getting tight later on, but for now, it seems to work. But how do you connect to a place like this forum, for example? Well, you enter the text address as
htt ps://www.mac-forums.com/forums/apple-notebooks/352125-links-2.html#post1828995
NOTE: I had to add the space in "htt ps" to prevent the site from converting it to a URL and then not linking.
That name, however, means nothing to the software that is trying to connect. It needs the NUMBER of that location. To find that number a Domain Name Server (DNS) is consulted. DNS is a protocol used world wide where text names are converted to the actual numeric IP number for the location. When you have 192.168.1.1 as a DNS entry, that means that when you type in any address, or click on any text link like that one, that name is passed to the router at 192.168.1.1 for resolution to a number. The router then passes that request to whatever host your ISP is using for DNS. Eventually a DNS resolver will have the answer and will ship the address back down the line until it ends up at your router, who will send it out to your computer at 192.168.1.3. Your connection can then be made between you and that remote device. It's a bit like looking up the telephone number of someone you want to call but you don't have the number, but on a huge scale and at very high speed.
So, your system is set up by your router with an IP number in the range of 192.168.1.x, connects to 192.168.1.1 for name resolution and is connected to the internet through a different number that the modem/router has within the ISP network.
I know that's more than you asked, but sometimes it helps to have at least some understanding of how it all works.
FOR THE NETWORK ENGINEERS: Yes, I know that 192.168.x.x can have more addresses, but for this discussion his router is using 192.168.1.x. And yes, I know I greatly simplified the DNS process. And yes, I know about IPv6. And NAT. But this is long enough already!