Indeed, I have just confirmed that "schmelzkäse" is the official translation for "processed cheese", though Vorpal's translation is spot-on in a literal sense.
I have used it before for some sort of meatball sandwiches. The story behind it is that back when I was growing up, my father sometimes used to make some German style pork meatballs, and I had the idea of using them for some sort of burgers back then, using regular bread rolls and some of that processed cheese among other toppings (usually onions, sometimes some roasted onions in addition, bacon, and possibly some barbecue sauce). Also, the meatballs were usually cut in half for that.
We may have used that cheese because it just happened to be around when I first tried it, but it stuck. Even though I'm now making "proper" burgers pretty often at home, I still sometimes have a craving for those old meatball sandwiches in the style my father used to make them - well, I had the sandwiches back then, my parents just ate those meatball as they are. In fact, that's the reason I bought that cheese, I wanted to make them some time again.
Here's what they look like:

And here without the cheese:

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