Functions
Functions are objects that store a collection of commands (routines) that can be reused in different ways from within the database system itself to external languages or programs.
Procedures
Procedures are almost like ordinary functions except for the fact that they can't return values as functions do.
Triggers
Triggers are objects associated with a table that are used to execute operations stored in special functions when some operation (or event) happens on a single row or over the entire table.
Event triggers
Event triggers work like ordinary triggers in the way they are fired: when a specific event occurs.
Rules
Rules are objects that store additional SQL commands executed whenever a select, insert, delete, or update is performed on a table.
Aggregates
Aggregate functions are objects whose main goal is to compute a single result from a set of input values.
Languages
Languages are the basis for constructing functions and procedures in a database.
Transforms
A transform, as stated by the PostgreSQL docs, specifies how to adapt a data type to a procedural language.