The LKM framework is a means to compile a piece of kernel code outside of the kernel source tree, often referred to as "out-of-tree" code, keeping it independent from the kernel in a limited sense, and then insert it into or plug it into kernel memory, have it run and perform its job, and then remove it (or unplug it) from kernel memory.
The kernel module's source code, typically consisting of one or more C source files, header files, and a Makefile, is built (via make(1), of course) into a kernel module. The kernel module itself is merely a binary object file and not a binary executable. In Linux 2.4 and earlier, the kernel module's filename had a .o suffix; on modern 2.6 Linux and later, it instead has a .ko (kernel object) suffix. Once built, you can insert this .ko file – the kernel module – into the live kernel at runtime, effectively making it a part of the kernel.