The ANALYZE command in PostgreSQL scans a table's data or a sample of it to collect statistics about the columns. These statistics include information such as how many null values exist and how many distinct values are present. After collecting this data, ANALYZE updates the system metadata where the query planner reads these statistics. This helps the planner make better decisions about how to execute queries efficiently. The process starts when the command is issued, then rows are scanned, statistics are calculated, metadata is updated, and finally the command finishes. Sampling is used to save time while still getting useful statistics. If statistics are outdated, the planner may choose poor query plans, so running ANALYZE regularly is important.