Usability is a measure of the experience of the user when interacting with something.
In the case of web sites, especially government ones, think of it this way. If information is not organized using a structure that most people can easily understand, navigate, and use quickly and intuitively, the customer is being given poor customer service. If this customer is a member of the public , he may leave the site without something it is our job to provide, possibly even disillusioned and frustrated. If this customer is a state employee , the extra time he spends having to remember where things are on a poorly designed site, and figure out how to use features that take 5 screens to do what could have been done in 2 is all an unnecessary, and direct, cost to the taxpayer. Web site usability testing attempts to quantify the usability of a web site.