In a dictionary sense, a twerp is a person regarded as insignificant and contemptible, and in an idiomatic sense it means a small individual or child. The word is most frequently used in an affectionate sense, as in "You silly twerp!" when one has done something unfortunate, like dropping a full milk bottle as a small child.

So where did the word come from? Some point to a letter written by J.R.R. Tolkien to his son Christopher Tolkien on the 6th October 1944. Tolkien refers to one T.W. Earp (President of the Oxford Union before the Great War), who he calls "the original twerp". In point of fact, the word was in use in the Army as early as 1925, and one source points to a date of 1874.

My efforts to prove that it is also a pregnant goldfish (as oft rumoured) have so far come to naught. They may be thinking of twit.

www.abc.net.au/classic/breakfast/stories/s736443.htm
http://www.etymonline.com/index.php?l=t&p=18
http://www.straightdope.com/columns/020329.html