First of all, you need to understand so many other CS concepts to understand a compiler, so we can take the reverse statement: If you understand how compilers work, then you've got to have a pretty good grasp of how computers work in general. Second, when it comes down to it, everything that you do is built on compiled software, and you've got a series of abstractions starting with physics, transistors, logic gates, processor architecture, the OS, user-space software, etc. Essentially, the compiler provides that abstracting links between the hardware and the software, and when it comes down to it, if you don't know how an abstraction is implemented, then you don't really know how it works.