An eager beaver was an idiom used to describe an individual who had full of energy and a good attitude.
In 2365, Doctor Katherine Pulaski explained to Data what the word "eager beaver" meant while viewing a virus, stating, "Well, in this case, "eager beaver" refers to some overachieving genetic engineer who – probably because of lack of anything better to do – has forced this strain of virus to mutate just so he can see how bad "bad" can get." (TNG: "The Child")