Learn Icelandic: Við mætum seint vegna umferðarinnar. - We arrive late because of the traffic.

This is because of the preposition vegna (because of). Vegna is one of the prepositions that force the noun following it into the genitive case. Here, "the traffic" is in the genitive case with the definite article attached.

How do we build the genitive form umferðarinnar?

The base word is umferð (traffic), which is a feminine noun. Its genitive singular form is umferðar. To say "the traffic", we add the genitive feminine definite article -innar to the end, giving us umferðarinnar.

The translation says "arrive", but I thought koma meant to arrive or come. Why use mætum here?

While you could say við komum seint (we arrive late), mæta (to show up, attend) is extremely common in Icelandic when talking about arriving at a planned commitment like school, work, or a meeting. Við mætum seint implies "we are showing up late" to a specific event.

Is seint related to the adjective seinn (late)?

Yes! Seint is the adverb form of seinn. Because it is describing the verb mætum (how we arrive) rather than a noun, it takes the neuter/adverbial form seint.