* The memory hierarchy (registers, cache, memory); really all programmers always need to know the memory hierarchy and Meltdown just sort of reinforces that.
* The basics of kernel memory management (kernel memory is mapped into userland processes and protected by page table permissions checks).
* Very basic assembly language (basically what a variable assignment and an "if" statement compile down to).
* The idea of pipelined CPUs, the idea that on modern CPUs the registers you see in assembly instructions are actually renamed from a larger invisible register file, and the distinction between instruction execution and retirement.
If you've got this I think you can just read the paper: https://meltdownattack.com/meltdown.pdf. It's really well written. In particular: I don't think you need to understand much about timing attacks. The Flush+Reload paper (you can just Google it, it'll be the first result) is also really well written, but you'll be fine in the Meltdown paper without having read it.