See the main NATS Interview Process thread for most details on the tests.
[Think the main thread should be made into a sticky.]
Basically, the diagramming is checking your ability to not only follow
an instruction, but rather a series of instructions, some of which may counter previous instructions you have given [Thus testing you can keep a picture of the entire thread of instructions].
Think of it this way.
Your merrily watching an aircraft going due south. Another is on a reciprocal heading, coming straight towards it, at the same level.
Your first thought is to climb [for examples sake] one aircraft. Mentally, this option becomes position 1 in your plan. However, looking at traffic further down the line, you realise you cannot climb either, so you cancel your previous instruction, and choose something else.
Fine, but then a third aircraft appears that completely throws your plan out the window [it wasnt a good plan to start with
]. You have to remember what you did do, why, and what you now need to do taking in the new information, which may cancel or alter your previous instructions.
Ok - maybe not the best example, but hopefully it helps explain why the diagramming is there, and what type of thing may be being looked for.
Good Luck!