There are several differences between the Norton Core and a normal router.
1. Deep Packet inspection. From TrustedReviews.com:
The Core is a combination of Symantec's pre-existing security knowhow and some new features we’ve not seen before. The router will inspect every packet of data that passes through it for known pieces of malware and other naughties. This is a common feature in business networking products but is seldom found in kit for use in the home.
In short, it's a kind of firewall which is right on the entrypoint to your home, so it filters all traffic going to and from your home. Therefore, even if an individual computer's security is compromised, there is a second line of defence. As @jpmc26 mentioned in the comments below, it is certainly not a fail-proof security wall: malicious hackers can take other routes. However, it helps tighten up the security on your network in case the security on an individual device is compromised temporarily.
2. Frequent updates. According to the Norton Community, updates are run hourly, meaning that security compromises can be rapidly dealt with on a home level.
3. Multiple networking. You will be able to set up more than one network, so that any hacking would have to move through your router to another network, allowing for more detailed screening. Back on the Trusted Reviews page, apparently...
You'll also be able to move your most vulnerable devices, such as smart home kit, onto a completely separate network, making it much harder for a compromised device to open the door to the rest of your home network.
4. Security score. The Norton Core is constantly monitoring all individual devices on the network to feel out any security leaks on individual devices, such as out of date devices. From Norton's Website, which you referenced:
Core monitors data from your entire connected home, identifies security issues, and sums it all up in a single, powerful number. If there’s ever a problem, Core jumps in with real-time insights and tools to get you back on track.