not technical - what is data roaming?

Turning data roaming off only stops mobile data. Calls and texts abroad can still roam and get billed, so if you want nothing charged at all, airplane mode with wifi switched back on is the safe setting.

It just means using mobile data on somebody else's network instead of your own carrier's, normally because you've left the country. The phone still works exactly the same, your carrier just bills you for it, and sometimes heavily. Wifi is not roaming, so hotel wifi costs you nothing extra. If you're travelling without a roaming add-on, turn it off before you land - apps keep syncing in the background whether you touch the phone or not.