Word order in Esperanto generally follows a certain pattern, but it doesn't actually matter because you can tell what's the actual subject, verb, etc. based off what the endings are. So this is "the woman kisses the man" and not the other way around because "viron" has the accusative ending on it (the -n), showing it's the object and not the subject. Virino has an -o at the end, showing that it's the subject of the sentence.
Actually, some Esperanto courses put much more emphasis on non-Anglo word order.
Lernu.com starts moving the subject and object around right after they introduce sufficient vocabulary to construct a sentence. Lernu makes it seem like it is strictly a matter of preference in Esperanto. For them, one form is as common as another. I was surprised to see so much subject/verb/object structure in Duo lessons.
It certainly makes it a lot easier for this Anglo to deal with.
It is not passive.
The word order changed, but the woman (the subject) is still actively kissing the man (the direct object). The instance of the direct object taking the "n" ending (e.g. viron) serves to make the word order of a sentence more free-form without confusing anyone as to which is the subject and which is the direct object.
If it were passive, the man would become the subject (e.g. "The man is kissed...").
Passive version would be thus:
"La viro estas kisita de la virino."
"The man is kissed by the woman."
NOTE for this passive construction:
Both the subject (man) and the prepositional object (woman) are in nominative case (i.e. both take the "O" ending: viro, virino).
Action is in the present, and is completed (i.e. "is kissed," as opposed to "is being kissed").
Because when a noun becomes the direct object (the object which receives the action of the verb), you add an "n" to the end of it.
One reason this is done is that it allows you to change the word order of a sentence without confusing the subject with the direct object.
This sentence can therefore be written either of two ways:
La virino kisas la viron.
La viron kisas la virino.
Both of them translate to "The woman kisses the man.
In the future, please browse the thread for answers to your question before asking, since it is likely to have already been answered.
One last thing:
Yes, kind of. I assume that this is influenced by Germanic languages. In German, you can theoratically put any object at the beginning, since their ending describes the case (Nominative, Accusative, Genitive or Dative), the role they play in the sentence. Be happy Esperanto only has 2, AFAIK.
Some poetic licence but also a reflection of the closeness to the Teutonic roots of English. As time passed and Latinate structures became dominant, such arrangements now seem very unusual.
In Shakespear's time such patterns were not as attention grabbing as they are now. Not typical speech, but with more gravitas because of it's invocation of tradition.