foreign key example:

an employee database:

employee table
department table

the employee table would hold employee specific data such as salary, and other employee info for all company employees.

the department table would hold data specific to the company’s departments

th employee table might have a key called department_id, which could point to the primary key of the department table (perhaps called department_id, id, etc)

lets say we adjust the name of a department – now all employees in that department will have a different department name showing by their name in a report of employees and their departments.

lets say we change the department_id key value for some employees to a different department_id value – now a report which lists the employees in that department will be affected accordingly.

this is foreign keys. a consequence of foreign key constraints is that you cannot delete a specific key in the foreign table if any rows in the linked table point to that specific key.

triggers are a whole different story, and they dont necessarily impose any constraints on the data of tables you use them on, as there isnt a real relationship between them. you could use a trigger, for example, to update the salary of everyone affected in a specific department, if a minimum salary amount stored in the departments table is increased, and you would otherwise have employees whos salary is below the department minimum. if you have a foreign key relationship between tables, this kind of a situation might have to be updated with a trigger, as foreign key constraints will not update data in another table.

these are just crude examples, as triggers have much more useful purpose, i just cant think of a practical example right now, and most databases have far more complex databases than just an employee and a department table, but hopefully this helps.