The Snowflake data platform organizes data stored in tables using databases and schemas, which are similar to traditional relational database concepts. A database is a logical grouping of schemas, while a schema is a grouping of database objects. Together, they create a namespace that can be inferred automatically or specified manually. Snowflake allows sharing of database objects with other accounts through "shares", providing data privacy protection. Data manipulation in Snowflake is done using the SQL-based data definition language (DDL), and storage works by storing individual micro-partitions of rows as groups of columns, optimized for big data processing. This internal architecture accelerates query performance without unnecessary scanning, making it a scalable solution for analytics workloads.