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Word embeddings are computational language models that represent words or concepts as positions in an abstract many-dimensional meaning space. Despite a growing range of applications demonstrating their utility for sociology, there is little conceptual clarity regarding what exactly embeddings measure and whether this matches what we need them to measure. Here, we fill this theoretical gap by demonstrating that embeddings operationalize context spaces, where words’ positions can reflect any regularity in usage. We then closely examine sociologists' embeddings-based cultural measurements to argue that most sociological scholarship is instead implicitly interested in capturing concept spaces, where positions strictly indicate socially meaningful conceptual features (e.g., femininity or status). Because meaningful features yield regularities in usage, context spaces can proxy for concept spaces. However, context spaces also reflect regularities in the surface form of language--e.g., syntax, morphology, and dialect--that are irrelevant to most sociological investigations and that can bias cultural measurement. We draw on our theoretical framework to develop novel implications about how to successfully measure cultural meaning with embeddings.