What's immediate superset?
Immediate often occurs simply to say that there are perhaps many supersets, e.g. when we have a tree like structure. There is also for example, the converse, an immediate subset.



Example

Set A has a superset B, and that superset has its own superset C. In this case, A must also be contained within C, but the set B lies within that realm and so is the immedaite superset of A.

Perhaps it is best visualised with a Venn diagram, where B is the immediate superset of A and equally the immediate subset of C:





There is some discussion here on Cross-Validated too, where the selected answer shows some further usage of the term (albeit in a slightly different context). Have a look at this source for some usage of the term, which leads you to my understanding.