Multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems.
Multinomial Logistic Regression
In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).
Multinomial logistic regression is known by a variety of other names, including multiclass LR, multinomial regression, softmax regression, multinomial logit, maximum entropy (MaxEnt) classifier, conditional maximum entropy model.
Source: http://en.wikipedia.org/wiki/Multinomial_logistic_regression