It's not final yet; the parties can appeal (at least they can if it was a contested divorce). Once the period for lodging an appeal has passed, or any appeal lodged has been resolved, the judgment (or decree, or decision) will be final. At that point it is to be reported to the Civil Registry.

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Note added at 1 hr (2017-05-05 19:23:46 GMT)
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So "Firme esta resolución" is short for "Cuando se declare firme esta resolución" or "Una vez firme esta resolución". Another variant you find is "firme que sea esta resolución". They all mean the same thing: it refers to future time.

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Note added at 7 hrs (2017-05-06 01:36:52 GMT)
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A couple of further points. First, another question makes it clear that this is not a contested divorce; it is a divorce by mutual consent. Under the new procedures introduced in Spain in 2005, this is a very quick procedure. The spouses present a joint petition and a settlement agreement. They are summoned to confirm their intention to divorce before the judge. Assuming the judge approves the proposed settlement, that it: he/she immediately delivers judgment.

This judgment is appealable:

"Una vez sea firme la Sentencia, lo que ocurrirá a los 5 días de su notificación si no es recurrida por ninguna de las partes, en ambos casos, separación y divorcio, se produce la suspensión de la vida en común, en el supuesto del divorcio, además, supondrá la disolución del vínculo matrimonial y la posibilidad de poder casarse nuevamente."
https://www.leyfacil.com/saber_mas_divorcio/

So Sandro is right that a "sentencia firme" is non-appealable. However, in this very streamlined procedure I'm not sure it's really necessary to call it "final and non-appealable", correct though that would be. There is just a summary judgment, a very brief period for appeal, and confirmation. Personally I think "final" is enough in this context. But I would have no objection to adding "and non-appealable" (that's how it's usually expressed in British English; unappealable, with one l, is standard in the US).