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The video tutorial by Cohere AI explains the concepts of word and sentence embeddings, which are crucial for large language models. These embeddings enable computers to understand and process language by converting words and sentences into numerical representations. Word embeddings associate each word with a list of numbers, while sentence embeddings do the same for sentences, capturing contextual meaning. This process is not manually done but is instead executed by a neural network model, which analyzes the context in which words and sentences appear together. As a result, words and sentences that share similar contexts are placed closer in the embedding space, yielding impressive outcomes in language processing.