I'm looking at job requirements for Jr. web Developer positions. Some jobs need "Great typography and layout skills." What does typography mean? What skills are they exactly looking for?
"What does typography means"
Typography refers to type. The art and craft of setting and using type. It can also refer to lettering design, and the design of type (the letterforms) itself.
It's a little odd (but not unheard of) that they are asking for a 'developer' with 'typography skills'. Based on that, I'd say they are looking for a talented graphic designer with strong front-end web development skills They may legitimately be looking for that role, or this may be one of those types of job descriptions where they shot-gun the requirements list hoping to hire an entire art and IT department in one Jnr position.
I agree with DA01's answer. In addition:
Having typography skills means things like: understanding the difference between serif and sans serif typefaces; knowing which typefaces to use for headlines, which might be great for blockquotes, etc. Which fonts go together well (for headlines and body).
Knowing the major categories of typefaces: oldstyle, transitional, modern, decorative, calligraphic (or handwriting), grunge, etc. Being able to recognize well-respected classic faces like: Garamond, Futura, Goudy, Helvetica, Baskerville, Bodoni, Frutiger, etc. on sight.
Also understanding leading, the space between lines of type. Which fonts need more, which need less, optimum line lengths at a specific point size (for setting type sizes of main columns vs sidebars). Understanding the terms I just used.
As more fonts are able to be used on websites (using Google fonts, @font_face, Typekit, etc.) these skills come in handy for developers, as well as for designers.
If they want you be or become a themer: writing CSS styles from Photoshop, Illustrator or Fireworks files, then the skills I've mentioned would also be important.