It was sort of answered above, but I’ll try to put things into context.
First, C came first. As such, what C does is, sort of, the “default”. It does not mangle names because it just doesn’t. A function name is a function name. A global is a global, and so on.
Then C++ came along. C++ wanted to be able to use the same linker as C, and to be able to link with code written in C. But C++ could not leave the C “mangling” (or, lack there of) as is. Check out the following example:
int function(int a);
int function();
In C++, these are distinct functions, with distinct bodies. If none of them are mangled, both will be called “function” (or “_function”), and the linker will complain about the redefinition of a symbol. C++ solution was to mangle the argument types into the function name. So, one is called _function_int and the other is called _function_void (not actual mangling scheme) and the collision is avoided.
Now we’re left with a problem. If int function(int a) was defined in a C module, and we’re merely taking its header (i.e. declaration) in C++ code and using it, the compiler will generate an instruction to the linker to import _function_int. When the function was defined, in the C module, it was not called that. It was called _function. This will cause a linker error.
To avoid that error, during the declaration of the function, we tell the compiler it is a function designed to be linked with, or compiled by, a C compiler:
extern "C" int function(int a);
The C++ compiler now knows to import _function rather than _function_int, and all is well.