A nagger is usually a woman. To nag means persistently fault-finding, complaining, or demanding. For example, sometimes a man just wants to eat an ice cream sandwich for breakfast, but if a woman is there she will probably give you her opinion about it. All you want to do is eat the ice cream sandwich but the whole time she is telling you how it's bad for you :(.

More context would be helpful, but if I had to guess, it's someone who nags, or constantly criticizes, scolds, or finds fault with someone.