Hand-drawn dolls are dolls that are drawn in an image editing program (such as MS Paint, Photoshop, GIMP, etc), as opposed to being put together on a dollmaker.
Pixel art is a form of digital art where the pixels are placed manually (instead of using tools such as blur or smudge which calculate pixel values automatically). See the Wikipedia page
for more information. (some hand-drawn dolls can also be considered pixel art)
From the FAQ
4. How do I make handdrawn dolls?
First you need a base - see this thread for a list of base sites. If you have a base but don't have any idea what to do next, then read some tutorials - a good list can be found in the Tutorials forum. After reading the tutorials, all you need to do is open up an image editing program and get drawing - make the clothes, hair, accessories, etc. Don't worry if your dolls are not very good, even the most talented dolls weren't perfect at first! And be sure to post your doll on this forum. We all want to see it!
If you're interested in making other kinds of pixel art, try searching Google for "pixel art tutorial".