The ivfflat algorithm in pgvector provides an efficient solution for approximate nearest neighbor search over high-dimensional data like embeddings. It works by clustering similar vectors into regions and building an inverted index to map each region to its vectors, allowing queries to focus on a subset of the data, enabling fast search. By tuning the lists and probes parameters, ivfflat can balance speed and accuracy for a dataset. Overall, ivfflat gives PostgreSQL the ability to perform fast semantic similarity search over complex data. With simple queries, applications can find the nearest neighbors to a query vector among millions of high-dimensional vectors, making it a compelling solution for natural language processing, information retrieval, and more. By understanding how ivfflat divides the vector space into regions and builds its inverted index, developers can optimize its performance for their needs and build powerful applications on top of it.