The YC idea matcher app uses semantic search to provide users with a list of similar companies that have invested in their startup ideas. It achieves this through the use of vector embeddings and vector similarity search, which allows it to understand the meaning behind user queries and retrieve relevant results. The app generates vector embeddings using OpenAI's Embeddings API and stores them in a Neon database, which is then used for similarity searches. The Postgres extension pg_embedding is used to perform these similarities searches efficiently. The app uses Next.js for its frontend and serverless edge functions on Vercel for its backend. Overall, the app demonstrates how semantic search can be applied to real-world problems using AI technologies like OpenAI, Neon, and pg_embedding.