What are the advantages of Skip-Gram methods?
Basically, skip-gram aim for computing the probability of a context given a word (it is CBOW that does the opposite). BUT, it does not simply learn a co-occurrence matrix, it compresses the information in a low dimensional space (for example 300 for a 100000 original dimension). By doing this, it learns continuous low dimensional representation for the words.

It is proved that word2vec actually factorizes a word-context pointwise mutual information matrix (close to the co-occurrence matrix). I think this article might give you a better understanding of the underlying processes.