What you get is a JSON string, with key/value pairs. This string tells you what are the availability conditions to be satisfied.
The first pair is "op": &
It means: the boolean operator is an AND. Another value could have been OR.
The operator tells you how the availability conditions should relate each other: either should all of them be valid (AND) or at least one of them (OR).
The second pair is "showc": true.
It means, I suppose (not sure): Show the availability conditions: true. Another value could have been, of course, false.
The third pair is: "c" (condition): array
The "c" key gives you, as far as I understand, a detailed description of the availability conditions. Let's go into details, here:
The "type" key tells you what type of field you are going to evaluate: in your first and second example it is a course module id ("cm"), with values, respectively, of 10889 and 9989. It means: "what follows has to do with course module 10889".
I do not know what the key/value pair "e":1 means, though. It could mean: "this course-module should be completed". Try yourself: you could change the availability conditions of some course-module and see what happens.
By the way, you can read this JSON object directly from the field availability of your DB table mdl_course_modules (or your_prefix_course_modules).
In your third example the type is a grade ("grade"), the ID of the grade is "3410", and the "min" (I suppose the minimum value) is "100".
Note that there could be other types: for example: "type": "date", or "type": "grouping". I am not aware of a list of possible types available, though.
