What is the function prologue and epilogue in x86-64?

The prologue saves the old frame pointer and any callee-saved registers and reserves local space; the epilogue restores them in reverse and returns — leaving the caller's state untouched.

This bookkeeping is what lets functions nest cleanly: each one promises to give the stack and callee-saved registers back exactly as it found them.

Standard prologue (with frame pointer):

pushq %rbp           # 1. save caller's frame pointer
movq  %rsp, %rbp     # 2. establish this frame's base
subq  $N, %rsp       # 3. reserve space for locals
pushq %rbx           # 4. save any callee-saved regs used

Standard epilogue — undo it in reverse order:

popq  %rbx           # restore callee-saved regs
movq  %rbp, %rsp     # release locals
popq  %rbp           # restore caller's frame pointer
ret

The leave instruction is a one-byte shortcut for the two middle steps — it's exactly movq %rbp,%rsp; popq %rbp:

leave
ret

Optimized variant: when no frame pointer is needed, the compiler drops the %rbp save entirely and brackets the body with just subq $N,%rsp … addq $N,%rsp.

Go deeper:

• Function prologue and epilogue (Wikipedia) — describes the prologue/epilogue bookkeeping directly.
• Felix Cloutier — LEAVE — LEAVE as the one-instruction epilogue shortcut.