What does the saying that "knowledge is justified, true belief" mean?

The formulation that "knowledge is justified, true belief" is basically a recasting of Plato within the framework of modern analytical philosophy, and scholars disagree about whether, in fact, in Plato knowledge can be described as true belief or contrasted to the notion of belief. In the many Platonic Greek texts, "doxa" (belief or opinion) is normally contrasted with "episteme" or knowledge, with one being temporary and contingent and the other timeless and absolute. 

The formulation of...

The formulation that "knowledge is justified, true belief" is basically a recasting of Plato within the framework of modern analytical philosophy, and scholars disagree about whether, in fact, in Plato knowledge can be described as true belief or contrasted to the notion of belief. In the many Platonic Greek texts, "doxa" (belief or opinion) is normally contrasted with "episteme" or knowledge, with one being temporary and contingent and the other timeless and absolute. 

The formulation of "justified true belief" accounts for how we come to have knowledge. We have many beliefs or opinions. For example, I might believe that Brand X oatmeal is cheaper than Brand Y oatmeal at my local supermarket on the basis of advertising and the price I pay at the checkout counter. That is an opinion supported by evidence and thus is "justified belief". One of my friends, however, points out that the Brand X package contains less oatmeal than the Brand Y one, even though the packages appear to be the same size. Thus my belief about the relative prices would be false. My friend's statement that "Brand Y oatmeal is actually cheaper than Brand X if you calculate cost per ounce" would be a justified true belief. 

The work of Edmund Gettier and a subsequent set of analyses challenge the analytical formulation of this definition of knowledge on the general basis that one can know something true about X and have a belief about X which is true but that the two may be independent of one another. The arguments against the formulation of knowledge as true belief by Gettier and his successors are known as Gettier problems.