The field of NLP is vast and complex. Any interaction between human language and computer science might technically fall into this category. For the sake of this discussion though, I'll confine NLP to analyzing, understanding, and, sometimes, generating human language.
From the beginnings of computer science, we've been fascinated by NLP as a gateway to strong artificial intelligence. In 1950, Alan Turing proposed the Turing test, which involves a computer impersonating a human so well that it's indistinguishable from another human, as a metric for machine intelligence. Ever since, we've worked to find clever ways to help machines understand human language. Along the way, we've developed speech-to-text transcription, automatic translation between human languages, the automatic summation of documents, topic...