Learn Hardcore Italian: Il cameriere torna e ci offre un dolce in omaggio. - The waiter returns and offers us a complimentary dessert.

Ci is an indirect object pronoun meaning to us or for us. Here it stands in for a noi. So ci offre literally means he offers to us.

Why is the verb offre in the third person singular?

Because the subject of the verb is il cameriere (the waiter), which is third person singular. If the waiters in general were offering, you might see offrono, but here we talk about the waiter coming back, so it’s offre.

What does in omaggio mean?

In omaggio means as a complimentary gift or simply free of charge. It emphasizes that the dessert is offered without cost to the customer.

Why is it un dolce and not una dolce?

Because dolce (dessert or sweet) is a masculine noun in Italian. Masculine singular nouns take un as the indefinite article, so it must be un dolce.

Could we replace ci offre un dolce in omaggio with ci regala un dolce? Are they the same?

They’re very similar but not identical:

Offrire focuses on offering something, often in a formal or service context (the waiter offers).
Regalare means to give as a gift, with a more personal or generous connotation.
Using ci regala un dolce would sound like the waiter “gives us a gift,” which is fine, but it’s slightly less idiomatic in a restaurant setting than offrire in omaggio.

Can in omaggio be replaced by gratis?

Yes, you could say ci offre un dolce gratis, but:

gratis is more colloquial and directly means free.
in omaggio sounds a bit more polished or promotional.
Both are understood, but in omaggio fits standard hospitality phrases better.