They basically have faces like Eastern emoticons. It's more or less like putting a simplistic smiley face on a recognized character design in order to make it look more juvenile/cute. It's also popular in mascots at times- see things like Qoo.
I'm not the kind of person that sees these things and flips out over how adorable they are, but I'm not such a hardass that I have to act irritated at the creation of anything that's meant to be puppy dog cute. It's the uncomfortable unison of childish cuteness and sexual overtones that makes moe annoying to me, and what I think tends to irritate lots of other people. I'm under the impression when people make fun of stuff that's purely meant to be cute it's done with a note of sarcasm, like making fun of Teletubbies or something.