Loyalty Research Center has a good definition of customer loyalty on their website:
Loyalty can be defined as customers continuing to believe that one organization’s products/services offer remains their best option. It meets their value proposition whatever that may be. They take that offer whenever faced with that purchasing decision.
Moreover, loyalty means hanging in there even when there may be a problem because the organization has been good to them in the past and addresses issues when they arise. It means that they do not seek out competitors and, when approached by competitors, are not interested. It also means being willing to spend the time and effort to communicate with the organization so as to build on past successes and overcome any weaknesses.
In a nutshell, loyalty means a customer wants to do business with you and does.
Source: http://www.loyaltyresearch.com/insights/thought-perspectives/customer-loyalty-what-is-it-how-can-you-measure-and-manage-it/