"Handcrafted" meaning that the image/animation has been painstakingly drawn rather than rendered in a 3D app. Not necessarily pixel-by-pixel as in the really old days, but that the artist has given thought to the pixel level of things.
The smilies on most forums and instant messaging programs, for instance, have had this "attention to detail" in their design. Same thing with most icons for toolbars etc. The various "emoticon packs" for MSN by Blue Mountain and other people is an exception though - many of them have pretty tacky graphics.
I'm probably a bit conservative, though - for this kind of thing I prefer simplicity and clean graphics; something like http://www.sherv.net/images/sc8.gif
is too "messy", although they're not the worst I've seen.
(gosh, I feel like a grumpy old man now