The fundamental requirement for a GNU/Linux system is a kernel and a filing system for it to execute things from.
The kernel is an autonomous piece of code that doesn't need any other files or libraries to get started, although without a root filing system it will simply stop after initialising the system as it no files to operate on.
The filing system can be loaded from a range of different hardware devices (hard disk, RAM, ROM, CD and NFS mount) and must be in a format that the kernel understands. For embedded systems it is often a RAMdisk. The kernel and RAMdisk both need to be loaded to correct places in memory and the kernel executed. This can be done in various ways, typically by loading over a serial connection or from local flash RAM.
In order to be able to load anything from anywhere some kind of bootloader must be present on the target hardware which knows how to load files and execute them. This can be installed in a physical fashion by inserting a pre-programmed ROM/EEPROM or flash chip, but is more usually installed using a JTAG port, which allows instructions to be executed from an external input, and thus an initial program loaded.
As there are so many possible boot scenarios we cannot describe them all in detail. We will describe only the most common (which are the most useful for typical situations) but also make the principles clear so you can do something more exotic if you need to.