The idea is related to Pareto efficiency. Under Pareto efficiency, an outcome is more efficient if at least one person is made better off and nobody is made worse off. Under Kaldor-Hicks efficiency, a more efficient outcome can leave some people worse off. Here, an outcome is more efficient if those that are made better off could in theory compensate those that are made worse off and lead to a Pareto optimal outcome.
The key difference is the question of compensation. Kaldor-Hicks does not require compensation, and thus does not necessarily make each party better off. Pareto efficiency does require making each party better off (or at least no worse off).
While all Kaldor-Hicks efficient situations are Pareto efficient, the reverse is not true. Conversely, though every Pareto improvement is a Kaldor-Hicks improvement, most Kaldor-Hicks improvements are not Pareto improvements.
The Kaldor-Hicks criterion is widely applied. For example, it forms an underlying rationale for cost-benefit analysis. In cost benefit analysis, a project (for example a new airport) is evaluated by comparing the total costs, such as building costs and environmental costs, with the total benefits, such as airline profits and convenience for travellers.
The project would typically be given the go-ahead if the benefits exceed the costs. This is effectively an application of the Kaldor-Hicks criterion, because it is equivalent to requiring that the benefits should be enough that those that benefit could in theory compensate those that have lost out. The criterion is used because it is argued that it is justifiable for society as a whole to make some worse off if this means a greater gain for others.