It means that somebody is nervous and restless. A very apt metaphorical use actually - imagine having to stand on a bed of pins and needles. You would not be able to stand still and would probably move nervously between both your feet. You are even a little (or lot) scared if you would get hurt if you take a wrong step. That is also how a nervous person reacts.
Students awaiting results, daddies-to-be outside a maternity ward, an interviewee right before the interview are all situations where people can be said to be on pins and needles.
Sometimes, when our parents or principals get really angry, we tend to be on pins and needles because we do not want to get it from them. So, we are nervous about the consequences and very vigilant about not making a mistake (or in some cases just praying that nothing goes wrong).
Students awaiting results, daddies-to-be outside a maternity ward, an interviewee right before the interview are all situations where people can be said to be on pins and needles.
Sometimes, when our parents or principals get really angry, we tend to be on pins and needles because we do not want to get it from them. So, we are nervous about the consequences and very vigilant about not making a mistake (or in some cases just praying that nothing goes wrong).