To compile C code, you need a bunch of different things: headers for the target system, a C compiler targetting that system, and a libc implementation to (statically or dynamically) link against. Different libc implementations are compatible with the C standard, but can be incompatible with each other, so it's important that you get the right one.

Cross-compiling with clang is complex because it's just a C compiler, and doesn't make assumptions about what headers the target system might use, or what libc it's using, so you have to set all those things up separately.

Zig is (apparently) a new language built on Clang/LLVM, so it can re-use that to provide a C compiler. It also makes cross-compilation easier in two other ways. First, it limits the number of supported targets - only Linux and Windows, and on Linux only glibc and musl, and all supported on a fixed list of the most common architectures. Second, building Zig involves pre-compiling every supported libc for every supported OS and architecture, and bundling them with the downloadable Zig package. That moves a lot of work from the end user to the Zig maintainers.

Like most magic tricks there's no actual magic involved, it's just somebody doing more and harder work than you can believe anyone would reasonably do.