I don't know everything that happens but I know a couple of things:
1. when our body feels our BG is going low, it releases adrenaline. For someone with a working pancreas, this acts as an insulin inhibitor sending a message to stop producing insulin. With diabetes and injecting insulin, adrenalin does not do the insulin inhibiting because we have already injected it so it is in our body. But we can experience the effects of high adrenaline which is the slightly manic behaviour, possibly stronger than usual, heart pumping faster, etc.
2. our brain needs blood sugar to work properly, when it does not have enough (I think this is about 2.8 mmol/l), it doesn't work properly which is what leads to things like inability to concentrate.
I am sure there is more than this and look forward to the other answers.