When systems are emulated does that mean they are literally recontructed in a 3D space? Is every circuit, transistor, chip, wire, and mechanical part recreated with thier physical properties as close as possible to the real life hardware? Is that how they do it?
As Theonik points out, this isn't really feasible for emulating a games console, but it is actually done in emulating old synthesisers. The lowest-level form of emulation that would actually be used in emulating games consoles would be instruction-level emulation, where the processor is emulated on an instruction by instruction basis. This takes the machine code of the game, which would be something along the lines of this:
Load data at memory address #00abc123 into register 1
Add register 1 to register 2
Increment address register 4
Store register 2 to memory at address register 4
etc., etc.
and actually goes through every instruction, calculating the results and keeping track of the registers and program counters and memory and soforth. This should give you pretty much perfect emulation, but it requires a substantially faster processor than the one that's being emulated, and gets particularly tricky once you start to think about emulating GPUs. Nonetheless, it's suitable for old consoles, and my guess would be that this is the way NES and SNES games are emulated on the virtual console.
Emulating more modern consoles requires higher-level emulation, which I believe usually involves emulating the API. This would mean identifying higher-level commands, such as
Draw a triangle with co-ordinates A, B and C on screen with texture D
and directly carrying out those commands, rather than the lower-level instructions they break down into. This can be a lot faster than instruction-level emulation, and has the added advantage of being able to change the way the game is rendered (at a higher resolution, for example). It (to the best of my knowledge) is what Dolphin and the Virtual Console N64 emulator rely on, for GPU emulation at least. It does bring compatibility issues with it, though. For one thing, it's tricky to get pixel-perfect emulation right, as you'd have to have a very intimate knowledge of how the GPU carries out the API commands to get it just right. Secondly, and more importantly, it breaks down when developers bypass the API and write their own assembly or microcode, which is something that happened a lot on the N64. This is the main reason that the N64 has so few games on the Virtual Console; they can't handle the custom microcode with their high-level emulator, but the Wii isn't powerful enough to run instruction-level emulation of the RCP (the N64's GPU). Dolphin has similar issues with a few of the Gamecube's more technically complex titles. In both cases the Rogue Squadron games from Factor 5 are the trickiest to emulate, due to the sheer amount of low-level optimisation that Factor 5 managed to squeeze out of each console.
One thing I hope Nintendo manage with the Virtual Console on the Wii U is full instruction-level emulation of the N64. We'd have to give up the increased resolution we get with N64 games on the Wii, but we'd get a much bigger library, which I'm sure would be worth the trade.