I'll try to explain at best and in simple layman term...

Root = is having administrative access to the phone, it is similar to "Administrator" user in Windows world and it is called "Root" in Linux. But it is not the same as Jailbreak in Apple. First and foremost, you're not in the jail by having Android. So nothing to break out from it

You're in a vast "open spaces" in which you will decorate it to become a garden, condo or whatever you wanted to do with it. By having this access, you can explore the system files, make a full backup of it, some modding on the themes, applications etc. But Root does not mean you can "start" installing ehem applications. It has been there since before rooting. Remember, you are in the "garden" not in the "jail".
Flash = is the action of replacing (upgrading or downgrading) the firmware, baseband or kernel.
ROM = actually it is best to call firmware, ROM in a technical short form of Read Once Memory. Since firmware is stored in the ROM thus they just called it as ROM for more understandable communication term.
Stock = original firmware that was supplied by the manufacturer.
Custom = modified firmware from "Stock" or recompile from "AOSP" source. Same goes to kernel as well.
Firmware = the operating system and applications but not the one you downloaded from market. This one will survived factory reset.
Baseband = the GSM / Modem / phone binary driver.
Kernel = the image / software layer which make the bridge between the hardware and the firmware. It consists mostly of device drivers, memory management, partitions etc.
Bootloader = the hardware booting image before kernel loading. The one which will present you recovery or download mode.
Recovery = recovery menu is for recovery purpose. This is the first level of recovery. Can be official or custom recovery like Clockworkmod or Teamwin recoveries.
Download mode = this is the second level of recovery. Mostly to flash back original firmware back to stock condition. Requires Samsung Odin software.
If you messed up with the bootloader, then your phone will be RM1K paper weight. But with recent development, there is a way to recover it by yourself but I haven't done it so I can't share the experience on this matter. Perhaps, someone may share his / her experience on this matter.
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