The interesting thing about word2vec is that is an unsupervised method that build vectors to represent each word in a way that makes easy to find relationship between them.

There is a video by the creator of Gensim on word2vec and frieds: https://www.youtube.com/watch?v=wTp3P2UnTfQ

We didn't include it, simply because it relies on machine learning and we wanted to show simpler methods.

Yes, I agree that the applications for word vectors are not made as clearly as it should be. One direct application is as the first layer of a neural network [1], which could be part of either a 1-dimensional convolution or a recurrent neural network. Using pre-trained word vectors is a form of transfer learning and allows for much more predictive models with smaller amounts of training data.

[1] https://blog.keras.io/using-pre-trained-word-embeddings-in-a...

Let me try:

Take the famous example of [king] and [queen] being close neighbors in vector space after generating the word vectors ("embedding"). If you then use these vectors to represent the words in your text, a sentence about kings will also add information about the concept of queens, and vice versa. To a far lesser degree, such a sentence will also add to your knowledge of [ceo], and, further down, [mechanical engineer]. But it will not change the system's knowledge of [stereo].

Essentially they are useful for comparing the semantic similarity of pieces of text. The text could be a word, phrase, sentence, paragraph, or document. One practical use case is semantic keyword search where the vectors can be used to automatically find a keyword's synonyms. Another is recommendation engines that recommend other documents based on semantic similarity.