The German connection others have raised is a good explanation for why I'd never seen this structure until a few years back. However, it's out there and in use now. It means, or can be taken to mean, "respectively", in much the same way that it's normally used in English.
The normal use for "respectively" is to signify that the items of two (or more) lists are meant to correspond to each other in one-to-one fashion. For example:
The hunters and gatherers brought meat and tubers, respectively.
This means that the hunters brought meat, and the gatherers brought tubers.
Now, the use of "resp." is a little bit different, but the purpose is the same. Instead of coming after the later list, it comes between items in each list. So your example:
For each of these problems (resp., tools), we start by presenting the natural concern underlying it (resp., its intuitive objective), then define the problem (resp., tool), and finally demonstrate that the problem can be solved (resp., the tool can be constructed).
- For each problem, we present the concern, define the problem, and demonstrate that it can be solved; and
- For each tool, we present its objective, define the tool, and demonstrate that it can be constructed.