To my understanding, recursion is a synonym of nesting, and it's distinctive when a child clause is center-embedded in the parent clause.
I believe below is an example of recursion:
The beautiful bird, singing in the cage, is mine.
In the example above, "singing in the cage" is the child clause, and "The beautiful bird is min" is the parent clause.
What I don't know is whether a sentence like this is considered to have a recursion:
The beautiful bird is mine, and it's singing in the cage.
Like a recursive sentence, this kind of structure can be extended endlessly, but I don't think it has a parent-child relationship between the clauses.