The PostgreSQL rule system allows one to define an alternate action to be performed on insertions, updates, or deletions in database tables. Roughly speaking, a rule causes additional commands to be executed when a given command on a given table is executed. Alternatively, an INSTEAD rule can replace a given command by another, or cause a command not to be executed at all.
Rules are used to implement table views as well. It is important to realize that a rule is really a command transformation mechanism, or command macro. The transformation happens before the execution of the commands starts. If you actually want an operation that fires independently for each physical row, you probably want to use a trigger, not a rule.
See also:
Database Designer for PostgreSQL allows to edit table rules.
Diagram Objects: Rule Editor