First, it's fun. Experiencing a new person from another culture gives you a lot to talk about.
It's also interesting in ways you don't expect. Language barriers (even when your student speaks pretty fluent English) can lead to trouble communicating. Best to speak slowly and using common terms if possible.
It's exhausting. I'm sure this is partly the adrenaline of the whole change/experience of meeting someone new, but for us it's an added exhaustion because we don't have other kids. I'll be honest: having to consider someone else in your house (besides hubby, who can pretty much fend for himself by now) isn't something I'm used to. It's OK, and I'm getting used to it, but it's definitely a psychological change.
It makes you think about things you hadn't thought about before. Your own politics. Your own country and quirks about the culture. How big everything is here. Which qualities and thoughts and values you want to communicate to your student (and which are better left unspoken).
And this is only the beginning. I'm sure there's much more in store (and hey, maybe a story idea or two as well). To sign off, some pictures:
Outside her adopted American high school