How to understand function recursion precisely?

Question

I am currently programming some divide-conquer algorithms, where function recursions are used everywhere, but I have very vague idea or no idea how exactly it works, and tha

Answer 1

A function calling itself is not different from a function calling another function: before proceeding it has to wait that the function it has called returns.

By the way, recursion might look elegant, but in general it's not the most efficient way of programming: it makes for example impossible to inline functions, so the overhead for context switch is guaranteed. There's always a more efficient way to obtain the same result of a recursive function. But for some problems a recursive implementation is more intuitive, and not slower in any significant way. The example you gave in the comments, merge sort, is a good one.

A couple of interesting discussion about this:
Way to go from recursion to iteration
Can every recursion be converted into iteration?

My final advice: do not go for recursive when the problem does not require this approach, for example when computing a factorial.