DuckDB is an embedded SQL database that can be used directly from C, C++ or other programming languages without separate server process.
It supports standard SQL and can be used to query, insert and manipulate data directly similar to other SQL databases like SQLite.
DuckDB provides data types, functions and queries similar to bigger databases but runs directly in-process without separate server.
Being an embedded database, it has smaller footprint than SQLite and faster for analytical queries with advanced optimizations.
Mother Duck is not a real database but just a fanciful analogy to refer conceptually to DuckDB which can be embedded or used like a mother to other programs.
DuckDB aims to combine advantages of embedded databases and big analytical databases for applications with SQL data needs.
It is a good option for programs that need local SQL data storage and queries without overhead of client-server databases.