Slab serif refers to a style of font that possesses serifs (similar to Times New Roman, Gentium, or Nimbus Roman). However, slab serif fonts have serifs that are blockish in nature, usually squared off at the ends (though Courier and a few others are rounded), in contrast to the thin or tapered serifs of the more traditional serif fonts.
Slab serifs are generally reserved for headlines and other similarly large-sized but short pieces of text. The strength of the serifs makes them hard to use in body text, though it does happen. The one exception to this rule is that many monospaced typewriter fonts make use of slab serifs. These fonts are generally fading from prominence in modern times, but they can still be found many places (like the Everything2 text areas).
Some well-known slab serif typefaces are: Nilland, Courier, Rockwell, DejaVu Serif, among many others.
I find slab serifs to be a niche font. They can work well in some large-format designs (such as posters) but they seem wholly inapplicable to web design or any sort of high word count production (like a newspaper). I do hear tell of The Guardian printing its body text in a slab serif face, so perhaps I am just reluctant to see something out of the norm, but slab serifs are not a favorite of mine.
That being said, there are some wonderfully well-designed slab-serif faces out there. I just can't see a good place to put text made with them.