"The woman kisses the man."
Translation:La virino kisas la viron.
There are verbs like sleep or breath or exist that rely only on the person doing the action. If I sleep I don't sleep any other person or I do not breath any other person (I could breath air, though). It is impossible for the verb exist to rely on someone else: do I exist you? No. That's not possible. Those kind of verbs are intransitive.
But there are other verbs called transitive, that mean that their action could rely on a second noun, known as the object. Per example: "I see the ball". I could just say that I see, but the verb allows me to see something, not like exist or sleep. Another example is "I kiss my girlfriend", where the action of kissing falls on the girlfriend; grammatically speaking, my girlfriend is the object of the sentence. In many languages this is called the acusative case.
When you use a verb and its action relies or falls into another (the object) the object and its modifiers (adjectives, but not the definite article "la") get the -n to the end. In the examples I mentioned, that would be:
"I see the ball" = "Mi vidas la palon"
"I kiss my girlfriend" = "Mi kisas mian koroamikinon"
Because of the -n at the end of the object, it is possible to recognize who does the action and who receives it. So it doesn't matter the order in which you write it. "La palon mi vidas" or "Vidas la palon mi" work just fine.
Hope I helped. Sorry for the long post.
The order doesn't matter. The -n at the end of the word defines that "viro-n" receives the action and since "virino" doesn't have the -n, it means "virino" is the one doing the action (for this case: she is the one who kisses). See my answer to kyyyker if you still don't get it ;)