Aren't there block diagrams in the user manuals?
It provides a means of accessing the target IC's scan-chains via JTAG or SWD protocols
The target IC can work fine without this access, you can program the parts in-situ using the methods described in app note AN2606, for UART connectivity AN3155.
You can use stand-alone debug pods, like the Segger J-Link, ARM U-Link, but these add cost and clutter compared to providing already attached, On-Board.
The integration of the debugger onto the NUCLEO and DISCO board allows for cheap, easy access, with a single board and cable. Something you can give a student, they can work on immediately in the lab, or take home.
The STM32F103 programmed with the debugger are not available in the sense of the ATMEL/MICROCHIP EDBG solution, but you can get some ST-LINK/V3MINI(E) type formats you can solder to your own development boards.