Prototype Theory (PT) is a core element of the linguistic approach called Cognitive Linguistic. It derives from cognitive psychology and tries to answer the question which principles are responsible for assigning a certain entity to a certain category.
The traditional view of category membership dates back as far as Aristotle who judged categories as being like containers where category membership is defined via a set of necessary and sufficient features. This approach is calld checklist theory since category membership is defined via features on a virtual checklist. In the seventies cognitive psychologists started to criticize that approach by highlighting certain problems of the Aristotlian view such as: Which properties go on the checklist? How do we rank the importance of the features on the list? And some categories are just very hard do define via a set of necessay and sufficient features as the category "game", for instance, as was shown by Ludwig Wittgenstein.
PT argues that category membership is not assigned according to a list of necessary and sufficient features but by a cluster of attributes of the most representative members. These members serve as cognitive reference points that are used to decide whether an entity belongs to a category or not. In this context it is important to note that an entity does not have to exhibit all the features of the cognitive reference points. A certain degree of representativity is enough which is decided by a so called goodness of example rating. According to this approach category members are linked by family resemblance i.e. all members share at least some features with other category members. Thus PT states that categories have more central and more marginal members. Taking the category "bird" as an example, a nightingale is a more central member than a penguin or, as one might also say, the former one is "birdier" than the latter. But there is no question that a penguin is and remains a member of the category "bird", if only a marginal one. We do not have a degree of membership but only a degree of representativity. Why something is prototypical depends on the relevance an entity has for a given cultural community as well as the frequency with which it is used. The more entreched an entity is the more likely it is to serve as a cognitive reference point.
Some categories are psychological more real than others. This level is called the basic level category which is maximally distinct i.e. it maximizes the within category similarities and the between category differences. At the basic level the highest amount of information can be processed using the least amount of cognitive effort which leads to perfect cognitive economy. An example would be the basic level category "chair". The superordinate category would be "furniture", one subordinate category "rocking chair", for example. Basic level categories are learned first by children and it is the level where categories are recognised the fastest.
Now, what should be the consequences of PT for lexical semantics? First of all only typical properties should be part of the definition of an item's lexical meaning. Secondly, we know now that there is no distinction between dictionary and encyclopaedic meaning. Meaning is always dynamic and flexible and never static as in a dictionary.