Question about language targeting.

When I set my targeting to Spanish, does this mean that my ad will be seen by people who search under the domain google.es, or does it work somehow differently?

I think that in this case only people with Spanish IP will see the ads, I am not sure about google's domain

Your ads will be shown to people who have their language set as Spanish in the Google settings. Nothing to do with the TLD. You can of course set your campaign to show only in certain geographies, only Spain for example or if you wanted, just Madrid. But they also have to have their language set to Spanish.

Your ad also will be seen if the user uses google.com, google.ca, google.com.mx or any Google's domain, to people who set their language to Spanish in the Gmail or Google settings.