It's explained in "IBM's Management Makeover" (Nov. 2004) in Fast Company magazine.
To begin with, the best executives no longer thought of the folks to whom they sold stuff as customers; they saw them as clients. The difference? "A customer is transactional," says Harris Ginsberg, IBM's director of global executive and organization capability. "A client is somebody with whom you have a longstanding relationship and a personal investment." It's no longer enough to sell a customer a server. An IBMer should be so focused on becoming a long-term trusted partner that she might even discourage a client from buying some new piece of hardware if it's in the client's best interest to hold off.
So a customer is a one-time sale. A client is an ongoing relationship, with additional sales from time-to-time as needed. We want a buyer to be customer again and again; that's a client. And check out that last part: We don't want to sell you something if we think you don't need it! Such a sale might be good for a customer, but not a client.
Personally, the term "client" kinda messes me up, because it makes me think of client/server and EJB clients. Then again, maybe IBM is and should act that way to its buyers, acting as a server providing services (hardware, software, knowledge workers). Anyway, I guess I'm just getting too caught up in computer-speak and need to adjust more to business-speak in this case.
Our CEO, Sam Palmisano, talked out the customer/client difference in this article in Fortune magazine, "Can IBM Get Great Again?" (but you need a subscription). Here's some guy talking about very much the same thing: What You Call Your Customers Matters.