What was a madrasa? What was taught there?

It is true. The word "madrassa" just means "school" and applies equally to secular public schools and the mosque's equivalent of "Bible study". You are probably thinking of the Wahabi madrassas which were extensively funded by the Saudi royal family not so much because the Saudi royals are all that religious but because it helps keep the religious nutbars from actively targeting them.

Madrasas still exist throughout the Islamic world. They are among the many religious, charitable, and educational institutions operated by mosques.

A School or College.

The one I attended taught oriental languages. I benefited from vastly lower tuition fees than would apply anywhere at home.

Madrassa is quite literally the Arabic word for school.