I’ll split it in two. This is my own personal interpretation, I’m not an official Zig anything, but I am an unofficial Zig proselytizer. 
Zig wants to support a lot of targets on a lot of hosts and provide a good development experience across all of it. One of the main features of “good development experience” is that selecting a target for building should be as easy as passing a flag to the compiler. Another is that installing zig should be trivial.
Depending on your exact compilation setup, this is very frequently not the case in C/C++-land.
gcc by design is compiled for the target you want it to support as well as the host, so to support N different targets you need N different installations.
I think this influenced how most C build system works as well.
In cmake, for instance, this means writing toolchain files, which is a short header/config-like file that tells the build system where to find your C compiler, environment, and dependencies for the different targets.
Where your compiler lives, how to install it, and how to access it differs by host platform as well, so this ends up with a whole lot of “if on host A find compiler for target B at location C” in your build scripts, and a whole lot of “if on host A install compiler B for target C following guide D” in your onboarding docs, which is super annoying to maintain and keep up to date.
Newer compilers like clang simplify a lot of that by supporting multiple targets, but you still need to make sure the installation you have supports the target you want, which isn’t always a given.
Zig says “this shouldn’t be so hard” and does a lot of things under the hood to make sure every installation has a compiler available with the same interface on every host supporting every target, and that the installed compiler has near-zero dependencies on the host system, which means invoking Zig to build a C program for some platform is the exact same (clang-compatible) command line interface, no matter how Zig was installed, and requires no other programs to be installed.
That’s what zig cc is.