A warm fuzzy is like a cotton ball with googly eyes. It's a furry little ball with tiny feet, usually no arms and these wild googly eyes.
Warm fuzzies are given as gifts to people as an act of gratitude, its symbolic of the feeling you get inside when somebody does something nice for you. When somebody makes you feel this way, you in return give that individual a warm fuzzy.
1) This hot girl I met at a bar the previous night woke me up with a blowjob and I had the most fantastic day as a result. In return, I e-mailed her a paintshop picture of a yellow "spray can" circle with big round dopey looking eyes and little feet. I scribbled "warm fuzzy says thanks for fellating me this morning"
2) I used a yellow marker to color a cotton ball and glued little googly eyes and feet I cut out of a cardboard toilet paper tube. I then gave it to somebody that went out of their way to help me at work. "Thanks, here's a warm fuzzy".