In order to understand Asm.js and where it fits into the browser you need to know where it came from and why it exists.
Emscripten takes in C/C++ code, passes it through LLVM, and converts
If the compiled Asm.js code is doing some rendering then it is most
likely being handled by WebGL (and rendered using OpenGL). In this way
browser but is almost entirely skirting the actual, normal, code