Bootloading: The process in which your phone boots up. Sort of like a computer. If a bootloader is locked, we're forced to use the ROM/OS that is already on there. If it is unlocked, we're able to install our own custom ROMs
S-Off: Security off. This is basically a function that you need in order to further customize/explore the inner workings of the phone. This is what we need to achieve in order to use undervolted kernels, which can save us precious battery life. Currently, it is on, which means we need a security key, a miracle, a leak from HTC, or a genius developer.
Unlocking: This refers to unlocking the bootloader, which means we can install our own custom ROMs, have root access, delete bloatware, etc. We currently have this thanks to the HTCDev tool. Verizon prefers to keep their phones locked, so that misinformed customers are "guided" into using Vcast, Blockbuster, and other apps that are locked in place.
Custom ROMs: These programs are built by Android developers (who we are very thankful toward for all of their hard work, no doubt). They can include things like vanilla Gingerbread, Sense-based user interfaces, and hopefully even vanilla ICS in the near future. (Vanilla refers to un-bloated, un-modded, and "pure" software.)
For your final question, the unlocking of the bootloader means that we now have permanent root. With permanent root, we're free to install custom ROMs.