Cross-compilation and toolchains
More than likely your MIPS box does not run Linux yet (why would you bother otherwise?). Therefore you will need another machine to build the kernel image. Once the image is built, you need to download this image to your MIPS machine and let it run your MIPS kernel. This is called cross-development. Your MIPS box is often called the target machine and the machine used to build the kernel image is called the host machine.
Cross-development is common for developing on embedded targets, because usually embedded targets do not have enough power or the peripherals to develop natively.