Word embeddings is one of the most powerful concepts of deep learning applied to Natural Language Processing. Any word of a dictionary (the set of words recognized for the specific task) is basically transformed into a numeric vector of a certain number of dimensions. All the rest, classification, semantic analysis, etc. is done from the aforementioned vectors on.
Here is a slide that explains this with a bit of algebra and some user friendly text. Download it and feel free to share.
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