JTAG is an in-circuit programming and debugging interface. It specifies the use of a dedicated debug port implementing a serial communications interface for low-overhead access without requiring direct external access to the system address and data buses. The interface connects to an on-chip test access port (TAP) that implements a stateful protocol to access a set of test registers that present chip logic levels and device capabilities of various parts.
JTAG interface is supported by many devices as a convenient way of rewriting firmware (specially boot loaders) when other methods fail. Using JTAG, the ROM memory can be directly written without desoldering it from PCB to program it using a specific programmer.
In most cases, you will need JTAG access to a device with a no longer working bootloader. Otherwise, if the bootloader runs, there should be easier ways of debricking the deice. Most of the times, a device with corrupt bootloader will not display any signs of working (i.e. no LEDs turned on in case of routers, no display on front panel of set-top-boxes). Nor any ports of the device will work (i.e. no serial port response, no network detected).