Statistical classification is a type of supervised learning algorithm which takes a feature representation of an object or concept and maps it to a classification label. A classification algorithm is designed to learn (to approximate the behavior of) a function which maps a vector of features [X1,X2,...XN] into one of several classes by looking at several input-output examples of the function.
An instance of a classification algorithm is called a classifier.
Classifiers may either be fixed classifiers or learning classifiers.
The study of pattern recognition consists of the construction and evaluation of classification algorithm. Please see that article for more information on classifiers.