I've never heard the term middleware before, is the term common? Is that a type of tool that a developer might expect me to be familiar with?
In the context of audio, Middleware usually refers to a pair of things. The first piece is a tool that you, the audio developer, use to create interactive audio content. It probably has a fancy GUI, and lets you work at a high, conceptual level to create things like interactive sound effects and music. With this tool, you take your wave fiels, etc and specify how they should be played in response to changes in the game. The tool outputs a number of files that you then hand off to the programmer. The second piece is a piece of code (software) the game developer includes with their game. That code knows how take the files created with the tool and play them back on the system (console, PC, phone, etc.).
For audio, "Middleware" usually means it's from a 3rd party-- but sometimes a game developer or game platform will have their own "middleware" tool for you to use.
If you're working with a medium/large developer, then they will probably expect you to know how to use the more common tools (FMod, WWise, etc.), or at least be familiar with how they work conceptually.
Btw, the tool part is almost always free-- the company that makes it makes their money by charging the game developer a license fee to use it.
if you're working on a small/indy game, it's less likely you'll be using one of these tools, since they generally cost $ to license for commercial uses.
Check out "FMod Studio", from FMod.org and WWise (from audiokinetic.com).