The PostgreSQL database management system implements polymorphism, a concept that allows functions or procedures to behave differently based on the data type of their input parameters. The "anyelement" pseudo-type enables declaring a function's formal parameter with a dynamically determined return value, while the "anyarray" pseudo-type allows creating an array of any data type. By utilizing these pseudo-types, developers can write polymorphic subprograms that adapt to different input values without having to create multiple versions of their code for each data type. This approach simplifies maintenance and improves flexibility in database applications.