Which ARM debugger hardware should I used to debug?
The programmers in question are external devices that allow a developer to connect a PC running the debug tools to the embedded processor under debug.  As stated in the quoted text in the question, the electrical connection is made via JTAG or SWD interface pins on the device.  Most often these pins are connected to a header on the PCB where the device is mounted.

The programmers shown below connect to the PC using USB.  Other programmers / debuggers can connect to the PC  using Ethernet or other electrical interfaces.



A representative list of available debuggers can be found in this Wikipedia Article.