In this context, it means it has rules, i.e. a recipe to follow per the context.
Combining both terms, means the system follows rules, as to generate content per the context.
An additional goal here is to be able to reproduce the same content, as long as you give it the same inputs, and thus the same outputs.
That inherently means it's not random, as it has rules, and is deterministic.
ProcGen is far reaching, and doesn't necessarily have to replace traditional level design; nor does it specifically apply to level design in the strictest sense.
Also, an example of a sufficiently robust procGen alg relating to level design is one that takes as input all the data of a level designed by a dev, and reproduce said level w/variations within specified ranges (not going over a pseudo alg here, too lazy heh).
Potentially taking a seed for base variation inputs to methods used to alter layouts, rules to prevent certain oddities from occurring, limiting type or range of edits to specific types of objects in the level, or specific methods as inputs (using this noise function for this layout placement pattern for this type of object, etc etc); thus producing variations that could very well be worthwhile.
However, even better is to introduce a learning method into this, say, a neural network being trained with this good and bad level data (or an evolution algorithm, as to produce variations based on good sets of levels); which could produce variations, while becoming better over time.
Since that process would be offline, I'd imagine the overhead is negligible, and using something like GPGPU it would reduce computation times to mere ms.
It can also apply to many other things, and there are plenty of patterns elicited by physical systems irl that can be reproduced by procedural techniques.
However, the mainstream use of procGen isn't necessarily to add to complexity, improve quality of content w/quality control, or to create more possibilities for fun; it's to curb their laziness… so I understand where you're coming from.
Although, not all developers are that way, and imo to sufficiently judge procGen is to have a full understanding of its complexities, limitations, and potentials.
Though, there are times when proc-gen is necessary, and times when a personal touch is necessary.
It really depends… on context.