What does it mean that my neck glands are swollen for so long?

Likely infectious... Swollen lymph nodes are typically related to recent or current infection. Can stay swollen for a couple of weeks. If they remain 'squishy and mobile' (meaning you can move them around like a marble under the skin), then they are likely fine. If they get bigger, or feel less well-defined and don't move around, definitely have checked out. Also dpends on what you mean by 'so long'.