Sentiment carries the unerlying meaning of any statement. We humans are born with a complex brain which helps us access the world around us through our cognitive abilities like Vision, Language, a new skill, etc. A human is born with an emotion. It is natural for us to recognise it.
Computers only understand numbers, and to quantify a sentiment into numbers is not possible. Hence Neural Networks which are modeled on human brain help the computers to recognise the underlying latent patterns. Human brain has millions of neurons which are cross connected and are finetuned bydefault. A computer has learn these finetuning values by training over a large amounts of data. Hence, to give computers the ability to understand the Natural World, we need to start thinking from the beginning... Literally.!
Sentiment Analysis is a branch of NLP which tries to capture the intention/sentiment behind the sentence.