Both C and Julia are compiled to machine code before they are executed. C is compiled Ahead Of Time, and Julia compiles new code as it runs, Just In Time, whenever a function is called with argument types it hasn't seen before.

Parts of Julia's library and compiler are implemented in C, but this actually isn't very relevant to the speed of the generated machine code that actually runs.

Statements about Julia being "on par" with C mean that if you write code in a straightforward way to solve some problem, e.g. "find the three largest even integers in a collection," then Julia is capable of generating machine code that executes with efficiency "on par" with the machine code that C generates.

The "straightforward" part in the last paragraph is actually important. You could in principle solve this problem in any language by writing your own machine code generator in that language, and then the distinction between efficiency of different languages breaks down. But usually you won't do that, and so usually the distinction does have some meaning.

GNU's assembler is implemented in C.

Because Julia has been carefully designed to allow functions to compile down to very fast machine code. There are a few important design choices that are necessary to make it possible to do this (type stability, etc) - there are a few talks about the design principles that went into making Julia.

However, numerical Python can be nearly as fast as C as well with very, very little additional work (using Numba means adding @jit on top of a function). The downside is that Numba only works on the 'numpy' subset of Python, basically.