Learn Icelandic: Þér var boðið veðmál við borðið. - You were offered a bet at the table.

This is the core of a ditransitive passive. The active verb bjóða (to offer) assigns the dative case to the recipient and the accusative case to the thing offered. When you make it passive, that dative recipient moves to the front to become the subject, but it stubbornly keeps its dative case.

What are the verb var and the participle boðið agreeing with?

They agree with the nominative object veðmál (a bet), which is neuter singular. In sentences with a dative subject, the verb and participle look past the subject and agree with the nominative object instead.

Veðmál is a neuter noun that looks identical in the singular and plural. How would this sentence look if it meant 'You were offered bets'?

The verb and participle would shift to match the neuter plural nominative object. The sentence would become Þér voru boðin veðmál við borðið. This dual agreement is a great way to tell if a neuter noun like this is singular or plural!

I thought location prepositions usually take the dative case. Why is it við borðið (accusative) instead of við borðinu?

While location often triggers the dative, the preposition við is a notable exception when it means 'at' or 'by' a physical object like a table. In these specific contexts, it consistently takes the accusative case.