Two that you'll see often are EQS and APM. EQS is extended quick settings - more stuff on status drop down so you don't have to wade through settings.
Here's an example -
APM, advanced power management. When you hold the power button, you get a menu with more choices, example -
A rom is a colloquialism. If it were truly read only memory, you couldn't change it. Feature phone operating systems some time back were burned into rom and couldn't be changed. Now, the full operating system is bundled into an easy to install payload, so that's called a rom.
The actual hardware being used is the same as an sd card, nand (not-and logic) flash memory, so installing becomes flashing and backing up becomes nandroid. That's where those terms come from.
The operating system includes a low level component called a kernel, said to tie hardware and software together. Mostly true. Your phone radios are a combination of hardware and programmable firmware. The kernel will tend to connect with the programmable radio firmware.
So, some updates will require radio firmware updates to preserve the correct working of the chain: phone app, Android virtual machine (Dalvik), Linux os, Linux kernel, radio firmware, radio hardware.
Radio firmware installation techniques vary by phone, might install like a rom, might require a different way. Often looks complicated until you do one.
Radio firmware is also called RIL for radio interface layer.
IME - a keyboard, probably making fun of Microsoft calling it an input method editor.
AOSP, Android Open Source Project, the code repository maintained by Google for pure Android. CM, CyanogenMod, is said to be an AOSP type rom, as opposed to a phone maker type rom.
There's a start, hope this helps!