[sauravjain]

I really like these posts by Sanjeev Arora :

1) http://www.offconvex.org/2015/12/12/word-embeddings-1/

2) http://www.offconvex.org/2016/02/14/word-embeddings-2/

For a more theoretical explanation :

https://arxiv.org/abs/1502.03520

[stared]

I learned about them just a few days before publishing this post (and I link to the second one, in the "technicalities" section).

Though, some statements about analogies should be taken with a grain of salt, see: Tal Linzen, Issues in evaluating semantic spaces using word analogies, https://arxiv.org/abs/1606.07736.