Warm and fuzzy means several things, I guess.
1) Having warm and fuzzy feelings (aka "the warm fuzzies") ...is when you feel good and happy inside. Maybe someone hugged you or complimented you on your shirt. That pleased, happy, warm feeling you get inside is feeling "all warm and fuzzy inside."
2) Someone can be "warm and fuzzy" in personality or in their behavior on a case-by-case basis..generally a nice and kind person (who is likely to make you feel warm and fuzzy inside), or someone acting nice and kind and affectionate. So, if someone is "warm and fuzzy" they're usually a kind, open person, positive person. (This can be changing, too. I.e., one day I might be all warm and fuzzy to other people because I'm in a good mood myself, but then tomorrow I'm back to being my usual reserved and closed off self

)
3) I suppose "something" can be warm and fuzzy, too. Like an action, attitude, movie or a song...or concert...but that's more obscure. The general idea is, again, that it is something or someone that gives you those warm and fuzzy feelings inside.
So overall, it's more psychological/emotional than physical. Things that are tangibly warm and things that are tangibly fuzzy feel good to the senses, physically... so the phrase is using that idea to figuratively represent how you feel emotionally.