A lot of the older phones needed to be rooted using an exploit, and thus people made applications that could root it from within the system. Since the Nexus phones are so easy to root without any exploits, all of the toolkits that are created are just using the ADB and Fastboot commands to flash a custom recovery and root the phone.
If you were rooted but didn't have a custom recovery, that would be simple to fix. If you had a custom recovery and needed root, that would be simple to fix. But with neither, I think you're going to need a computer.