NLP (Natural Language Processing) is the field of processing, synthesizing and understanding human language. Where as NUI (Natural User Interfaces) are ways of interacting with computers using Speech and Gestures.
NLU (Natural Language Understanding) is one of the most challenging areas despite the fact other related areas such as Speech Recognition, Speech Synthesis and Computer Vision have advanced a lot more. However, sufficient advances have been made in areas such as NLP & NUI that can help significantly augment applications.
Some practical examples of NLP & NUI:
Natural language search is ubiquitous and is used frequently.
Most documents leverage spelling and grammar checking, along with error correction and type ahead functionality.
Integrated speech and gesture based interfaces could radically transform interactions with computers.
My Views - Application of AI & Programming 