"Neither" and "nor" are the negative versions of "either" and "or".
It's easier to explain the positive versions first. They present a choice of options, of which you may only choose one.
- You may have either the cake or the chocolate bar
---- this means that the person is allowed one of the two items.
However, if you are forbidding someone from having them, you can use the neither / nor construction.
- You may have neither the cake nor the chocolate bar.