Continous bag of words claimed to be unsupervised, how is it working?
The CBOW approach is unsupervised because the network learns the distribution of word co-occurrences around each word, and this doesn't require labelling or additional input, just sequences of words. 

As Mikolov et al state in one of the original articles, "the training objective is to learn word vector representations that are good at predicting the nearby words; in another, Mikolov et al say their aim is "building a log-linear classifier with four future and four history words at the input, where the training criterion is to correctly classify the current (middle) word". So if you can see that for each sequence, you're taking 'x' words and training the network to predict one given the others, then no supervision is involved.

It's a little unconventional because it's not the output of the network which is important, but the weights that are learned during training - these are what is taken and used as embeddings in other tasks. 

Adrian Colyer does a great general write-up of word2vec here, and the explanation from Chris McCormick here is good and quite accessible.