1. Programmers are used to place your compiled or assembled program into the microcontroller. Another meaning of "programmers" are the people programming them

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2. Emulators are specially built chips that you could program fast easily and can stop anytime and anywhere in your code. The target processor is replaced with this emulation chip via cables and sockets. They run real-time and very similar in hardware and configuration to your target processor that they emulate. They have also special comms hardware attached that can communicate to the PC host. While debuggers are devices also similar to emulators but is a bit limited. They don't use the special emulation chip that is similar to the target but uses the target chip itself. The chip is connected to the debugger via JTAG or special pins intended for debugging only. Like in PIC, PG_CLK, PG_DATA and VPP are used to debug and is limited only to a single breakpoint.
3.Dev boards are pre-made boards with components and ready to run for evaluation of the chips or proof-of-concept designs. These boards also are used for quick prototyping and development. Most beginners use dev boards so they won't need to make a PCB by themselves and lessen errors in the hardware.