Learn Icelandic: Sum jarðlaganna eru mjög þykk. - Some of the geological layers are very thick.

This is an example of the partitive genitive. After a quantifier like sum (some), the larger group being divided is put into the genitive case to express the idea of taking a part from a whole. Here, jarðlaganna means literally 'of the geological layers'.

Since jarðlaganna is in the genitive, why aren't sum and þykk also in the genitive?

In a partitive construction, the quantifier (sum) acts as the grammatical subject of the sentence, so it takes the nominative case. The adjective (þykk) describes this subject, so it must also be in the nominative. Both take the neuter plural form to match the inherent gender and number of the noun they refer to (jarðlag, a neuter noun).

Why does jarðlaganna have the definite article attached?

When using the partitive genitive to say 'some of the layers', the noun in the genitive almost always takes the definite article suffix. Jarðlaga would be the indefinite genitive plural, but we need the definite form jarðlaganna to specifically mean 'of the layers' rather than just 'of layers'.

What words make up the compound noun jarðlaganna?

It is made of jörð (earth, ground) and lag (layer). In compound words, the prefix form of jörð often becomes jarð-. The second word, lag, is a neuter noun, which dictates the gender and the declension pattern of the entire compound word.