Rooting is the process by which you get access to a higher level of privileges on the phone. In the process, two applications, su (for command line/script application) and Superuser.apk (for Android application level use) are installed. When an Android application requests a higher level of privilege, the Superuser app is involved as a gatekeeper, to allow you to accept or reject the request. If you accept it, the application can go on to do what it needs/wants to do.
So why would you root? Light Flow is a very simple example - it's an app that allows you to customize the LED colors on your phone by notification type. Sounds simple, right? Well, on some phones, that requires higher privilege, so your phone would need to be rooted. That seems to be the case on the Nexus.
Another, more common, example would be the ability to install custom ROMS, with different feature sets and optimization, based on your needs.
After the Droid came out, carriers and phone manufacturers started encrypting the boot loader, to prevent hackers from installing new kernels, radio files, etc. Why would they do this? Largely because of applications that would allow you to tether without the carrier knowing about it, or allow you to "abuse" their networks in other ways. In other words, they want to maximize revenue in any way possible.
Unlocking the boot loader allows you to install new kernel software in the future, to overclock the device, to fix bugs, for optimization that may come along the way from the developer community. It also makes it simpler to install modified recovery software, which allows for system-level backups, and greater flexibility in dorking with your phone.
Rooting and unlocking are complimentary actions - you don't always have to do both - there are locked phones out there that are rootable, like the Bionic.
Doing either is technically a security risk. You could also, if you screw up, brick your phone, but there are ways to recover from that.
Doing either also *could* void your warranty. I'm not sure of the status of that with GN and Verizon.
I won't tell you to do either. I will tell you I did both the first night I had the phone. My choice.
Hope this helps.