This question is inevitable if one's major or PhD area is Comparative Literature. It sounds stupid to me when I hear it, but every person I've ever met who isn't an academic studying literature has asked me that question. What I compare are modernist poetics. Even though only one of my four books is a Comp Lit book, I still am a Comparatist, in my self definition.
To be that, you have to actually master a particular field. In my case, I am a Hispanist, and have only worked in Spanish depts, though my dream job, of course, is professor of comparative poetics and percussion. If I weren't a legit Hispanist I wouldn't be a good comparatist either. I hate comparatists who don't master any of their fields well enough.
You also have to master at least one other field. In my case, that is the literature of my own nation. So I could be an Americanist teaching courses in modern American poetry tomorrow, without having to retrain myself. I know Donne and Blake too, and some Shakespeare. I despise comparatists who can't hold their own in second field. I don't mean just knowing it at the wikipedia level, but being able to have actual ideas based on a specialist knowledge.
Thirdly, you have to have reading knowledge of some other traditions. I know French pretty well and can read novels and poetry and criticism in that language. A lot of Hispanists have really good French, but the reverse is more rare. I couldn't be French professor, though. I can read novels in Italian and Portuguese too. So maybe I am a romance philologist, though not a particularly erudite one. I might be as close at it comes for 2013.
Fourthly, you have to know something about literatures you don't read in the original. I know about Cavafy and Basho, or the history of translation of Chinese poetry into English. Y un largo etcétera...
The scholarly base for a comparatist should also include some intellectual history and philosophy. You should be able to teach Western Civilization, or comparative religion at a basic level, with a few weeks of prep time. You need some literary theory too.
So now on a chapter about Lorca's poetics of cultural exceptionalism, all this comes into view. It is handy, in the Heideggerian sense. I can talk about Cavafy and Barthes and Pessoa intelligently enough to make some comparisons. There's a depth there, one would hope, in that I'm not just looking up a Greek poet I just heard about the day before yesterday and doing some lame-assed "comparison."
Ironically, I might seem less qualified for comp lit type jobs than someone who "compares" more but doesn't have quite the depth of reading.