Anklebiter is an insulting term generally used to describe a small, insignificant, but annoying and irritating person. The term probably comes from the behavior of some small dogs, especially as seen by letter carriers. ("Nipping at one's heels" is another description of the behavior.)
The term is usually used to describe children. It is very insulting. For an adult to use the term to describe another adult would be incredibly rude.
An example of this term occurs in the movie Mrs. Doubtfire. The father, disguised as the domestic servant Mrs. Doubtfire and played by Robin Williams, uses the term to annoy and sow dissension among his children, in order to gain the upper hand in a conflict over homework.