Root access: Administrative access to the entire file system including the ability to change system files such as installing system-wide ad-blocker by modifying the host file on your device, or uninstalling system apps, such as bloatware that comes pre-installed on your device.
Unlocked bootloader: Even though it is possible in some cases to obtain root access without an unlocked bootloader, unlocking the bootloader is required to permanently root a device. This is because your carrier can simply unroot your device with an OTA update. Typically devices sold by most carriers under a contract will have a locked bootloader, preventing you from installing other roms (another version of android such as CyanogenMod) or tampering with your device in any way. Obtaining bootloader access on these devices is generally obtained by using an exploit, so if you plan to root your device do not allow any more OTA updates from your carrier until you check the xda forums for what options you have for your device.
For generalized, yet more detailed information, start by checking out this excellent answer.
If you decide to root your device, start by reading - How do I root my Android device?
Also have a look at - I've rooted my phone. Now what?
However, make sure you always check the xda-developers forums for updated information on what rooting procedures currently work for your device before attempting any rooting procedure, as these things change all the time.