Those of you who have read Agent Kristin's blog may already be familiar with this clause (she's written about it here and, more recently, here). For those of you who haven't, it's like this: book publishers want to protect their interests in their authors, and the non-compete clause is an effective way of ensuring this.
Under the NCC, an author generally can't reproduce any material from the book named in the contract, since doing so would damage the publisher's sales or infringe on their newly acquired rights. Example: if Fancy Pants Publishing acquires your book, 99 Ways to Defeat A Ninja, and you try to have High Fullutent Press publish an excerpt, or a graphic novel version, or some such other work that incorporates material from the first book or competes with FPP's sales, you're in violation of their NCC.
Kristin's second post (above) raises an even more interesting issue, one I inadvertently touched on in Monday's post: namely, that if your agent has withheld e-rights (or graphic novel rights, or any other subsidiary right), the language of the newer NCCs may prevent you from exercising those rights with other companies. If Fancy Pants Publishing has your hardcover and trade paperback, they're not going to want to see you reduce their sales by publishing the graphic novel and e-book with High Fullutent Press.
Now, in the case of Styron, the contract language was too old to include e-book rights, so I imagine the NCC in that contract/those contracts isn't broad enough to include e-books, either. But if your agent specifically withheld e-rights after 1995 or so, the NCC language may be new enough to allow publishers to invoke it to prevent you from publishing your e-books elsewhere. Food for thought, at any rate, and I again invite any agents in the house to weigh in on this... well, weighty issue.