What's the difference/relationship between AVR and Arduino?
I've been interested in hardware programming recently, but I have not started yet.
I did some searching working, and have a vague idea:
Arduino is a combination of both chip and breadboard.
AVR is a single chip, and need to buy a breadboard to get started.
Is that statement true or false?
Answer
AVR is just an integrated circuit microchip, made by Atmel. It looks something like this: 
Although they can be used by themselves, it takes a bit of hardware experience and some support components.
The Arduino is an AVR processor running special code that lets you use the Arduino environment to program and upload code easily. All you need is a USB cable to program and communicate with it. It looks something like this:
(source: mitchellpage.com.au)
A breadboard technically looks like this, and can be helpful in doing things with an Arduino. It is not necessarily needed for either solution but it is useful.
If your asking these sorts of questions, you should checkout the Arduino tutorials at adafruit. They're very basic and will teach you what you need to know to get started.