Inspired by this question
How can I force GDB to disassemble?
I wondered about the INT 21h as a concept. Now, I have some very rusty knowledge of the interna
Int 0x21 is an x86 software interrupt - basically that means there is an interrupt table at a fixed point in memory listing the addresses of software interrupt functions. When an x86 CPU receives the interrupt opcode (or otherwise decides that a particular software interrupt should be executed), it references that table to execute a call to that point (the function at that point must use iret instead of ret to return).
It is possible to remap Int 0x21 and other software interrupts (even inside DOS though this can have negative side effects). One interesting software interrupt to map or chain is Int 0x1C (or 0x08 if you are careful), which is the system tick interrupt, called 18.2 times every second. This can be used to create "background" processes, even in single threaded real mode (the real mode process will be interrupted 18.2 times a second to call your interrupt function).
On the DOS operating system (or a system that is providing some DOS emulation, such as Windows console) Int 0x21 is mapped to what is effectively the DOS operating systems main "API". By providing different values to the AH register, different DOS functions can be executed such as opening a file (AH=0x3D) or printing to the screen (AH=0x09).