Learn Icelandic: Fjórða bókin er mjög góð.

Ordinal numbers in Icelandic change to match the gender of the noun they describe. Because bók (book) is a feminine noun, you must use the feminine nominative form fjórða instead of the masculine fjórði.

Why does bókin have the definite ending "-in" attached to it?

In Icelandic, nouns following an ordinal number generally must be in their definite form (with the "the" suffix attached). You literally say "fourth book-the" (fjórða bókin). If you just said fjórða bók, it would sound incomplete to an Icelandic speaker.

If the noun is definite (bókin), shouldn't the adjective góð have a weak ending like góða?

That weak ending rule applies when the adjective is right next to the definite noun (like in the phrase "the good book"). But here, góð comes after the verb er ("is"). Adjectives that follow a verb to describe the subject use the "strong" (default) endings. The strong feminine nominative form of "good" is simply góð.

How does this sentence show us the gender of the word bók?