The change in the noun form is known to grammarians as the
"accusative case". It is similar to the choice of pronouns in English whereby we say, "Jean hit me", instead of, "Jean hit I". If you can manage to get the accusative programmed close to the place in your mind that knows when to use "me", you'll remember to use that final -n at the end of the direct object (although, as we will see later, the accusative is not used after prepositions).
The accusative case makes Esperanto word-order more flexible. For example, the following two sentences,
Johano havas katon.
Katon havas Johano.
are identical in meaning (John has a cat), differing only in emphasis. The second version would be idiomatically translated as "A cat is what John has."
Information provided by the Esperanto HyperCourse Maintainer as part of the Esperanto HyperCourse.