The object is the thing a verb acts on: I read a book, I eat an apple. In Finnish the object has two possible endings, and choosing between them is how Finnish shows whether the action is whole or partial:

Total object: -n	Partial object: -a / -ä
Luen kirjan. — I'll read the book (to the end).	Luen kirjaa. — I'm reading a book.
Syön omenan. — I'll eat the (whole) apple.	Syön omenaa. — I'm eating an apple / some apple.
Ostan talon. — I'm buying the house.	Etsin taloa. — I'm looking for a house.

• Total (-n): the action is complete and affects the whole thing — you finish the book, the apple is gone, the house is yours.
• Partial (-a / -ä): the action is ongoing, unfinished, or about some of it — the partitive you already know.

The total -n looks just like the genitive -n — same ending, different job.