Introduction
Logistic regression answers yes/no. But often there are many classes: which of three iris species, which of ten digits, which of 50,000 words comes next in a sentence.
Softmax regression (also called multinomial logistic regression) generalises logistic regression to many classes directly — no need for one-vs-rest tricks. The same idea is the output layer of almost every neural-network classifier, including the language models that choose the next word. So understanding softmax pays off far beyond this topic.