what does an "architectural history company" do?

Probably historic preservation.

recommendation to OP.  Be honest and ask them what they would like you to know before you start?

For instance if you were in NYC, you could look-up various Landmark Preservation Committee sponsored or published books, some technical, some historical, check them out at the library or buy a few copies and become familiar presumably with 'preservation' techniques from detailing to municipal laws...

My junior year of college I interned with a historic preservation non profit. When asked similar questions, I shared the few art history courses I had taken so far as well as my passion for architecture. I mostly just had to demonstrate that I could research and write before being hired as an intern (the art history courses I had taken had nothing to do with the era/style of architecture I would be working with). During that internship I condicted a research project to update the organizations records of all relevant buildings within the national historic register. This involved researching previous records of each building and visiting each structure to photograph and write up descriptions of the state of significant architectural elements. The research was used to create a publicly accessible database and for an exhibit the organization put together the next year.

Thanks for the info! And yes, an architectural history company works mainly with historic preservation. There's certain laws in place (at least in California) that require a historic analysis of the area before any new development projects from a company like the one I mentioned, e.g. making sure an area where they want to build apartments has no historically significant buildings that shouldn't be torn down. 

See if your school's career office can help you craft your response. You want to sell yourself well, but without lying. And be ambitious in telling them what you want to do, but also flexible (are you willing to clean the fridge and answer phones if you also get to do some research and draft some memos?)

They'll probably want someone who is good at research (framing questions and finding answers to them--this doesn't have to imply a fancy methodology), writing, and taking care of details. That might get you in even without specific experience in this kind of firm or context.