Learn Icelandic: Bátarnir eru stórir.

The basic word for boat is the masculine noun bátur. To make it plural (boats), the -ur changes to -ar, making bátar. Finally, to say the boats, we add the masculine plural definite ending -nir, resulting in bátarnir.

Earlier I learned the boat is báturinn. Why does the attached the change to -nir here?

In Icelandic, the definite article (the part attached to the end of the word to mean the) changes based on whether the word is singular or plural. While singular masculine nouns in the nominative case usually get -inn, plural masculine nouns get the ending -nir.

Why does the adjective stórir (large) end in -ir?

Adjectives must match the gender, number, and case of the noun they describe. Because bátarnir is a masculine plural noun in the nominative case, the base adjective stór takes the masculine plural ending -ir, becoming stórir.