The people who've tried to define customer loyalty have usually approached it from one of two different directions - attitudinal and behavioral. Although each of these directions is valid, they have different implications and lead to very different prescriptions for businesses. (This is analogous, but I don't think it is precisely aligned, with Estaban Kolsky's distinction between "emotional" and "intellectual" loyalty.)
The attitudinal definition of loyalty implies that loyalty is a state of mind. By this definition, a customer is "loyal" to a brand or a company if they have a positive, preferential attitude toward it. They like the company, its products or its brands, and they therefore prefer to buy from it, rather than from the company's competitors. In purely economic terms, the attitudinal definition of customer loyalty would mean that someone who is willing to pay a premium for Brand A over Brand B, even when the products they represent are virtually equivalent, is "loyal" to Brand A. But the emphasis is on "willingness," rather than on actual behavior, per se. In terms of attitudes, then, increasing a customer's loyalty is virtually equivalent to increasing the customer's preference for the brand. It is closely tied to customer satisfaction, and any company wanting to increase loyalty, in attitudinal terms, will concentrate on improving its product, its image, or other elements of the customer experience, relative to its competitors.
The behavioral definition of loyalty, on the other hand, relies on a customer's actual conduct, regardless of the attitudes or preferences that underlie that conduct. By this definition, a customer is "loyal" to a company if they buy from it and then continue to buy from it. Loyalty is concerned with re-purchase activity, regardless of any internally held attitudes or preferences. In the behavioral definition, loyalty is not the cause, but the result of brand preference. A company wanting to increase customer loyalty will focus on whatever tactics will in fact increase the amount of repurchase behavior - tactics that can easily include, without being limited to, improving brand preference, product quality, or customer satisfaction.
For a variety of reasons, Martha Rogers and I have always preferred working with the behavioral definition of customer loyalty, because it's simply more useful and practical. You can observe behaviors, while you have to conduct polls and surveys to gauge attitudes. But this doesn't mean we consider attitudinal loyalty not to be important. Positive attitudes do tend to drive positive behaviors.
That having been said, defining loyalty purely as an attitude is just not useful. For one thing, attitudinal loyalty and brand preference are redundant, so why introduce a separate term at all? Moreover, an attitude can exist completely separate and apart from any continuing relationship on the part of the customer, and this simply flies in the face of the common English definition of the word "loyalty." Customer A and Customer B might have an equally loyal attitude for a particular product, but what if Customer A has never even consumed that product before, while Customer B has consumed it regularly in the past? Rather than "loyalty," a far more useful attitudinal concept to use is simply "preference."
But finally, in our view the concept of customer loyalty should have as direct a connection as possible to a company's financial results. That is, we ought to be able to "connect the dots" between whatever strategies and tactics a company employs to increase its customers' loyalty, and the actual economic outcomes of those actions. An enterprise should be able to see a clear and direct economic benefit of some kind, as the result of a customer's loyalty. Gupta, Lehman and Stuart's "Valuing Customers" paper for the Journal of Marketing Research (2004), for instance [you can download it for free here, from Gupta's list of papers] clearly analyzes the economic value of an increase in loyalty, in contrast to an increase in margin or customer acquisition efficiency.
If, on the other hand, loyalty is just an attitude, then it has no immediate economic result. Internally held attitudes have no intrinsic value to a firm, because there is no financial result to measure until and unless these attitudes are somehow manifested into actions.