This is a late work, probably painted when Velazquez held a prestigious court appointment, and the circumstances of its commission are somewhat mysterious. However, the general scholarly view is that it is an allegory of artistic creation, with the myth of Athena and Arachne in the background of the tapestry workshop underscoring this interpretation. See below. (You'll need to read up on the myth, too.)
Velazquez was an extremely important representative of the Spanish Baroque, though his work was much influenced by his study of Italian Baroque developments. I've added another site on his career in general.
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