Ankusa (Goad) is an important weapon in the hand of Ganesha. Goad is held on the upraised right hand of Ganesh – not all artists follow this rule. So you will see Ganapati images with or without goad. Symbolically, goad assures a devotee that Ganesha will remove all the obstacles and difficulties.
Ganesha also uses the goad to pull out people who take the path of Adharma. Just as a mahout uses the goad to control the elephant, Ganesha uses it to pull people towards dharma. Symbolically, Ganesha will only bless those devotees who are on the path of Dharma. For those that follow Adharma he will create several obstacles to make them realize truth.
It is also believed that goad is used to give a hint to the devotees to understand the need to severe attachments.