Historically, most people have favoured their right hand, with the result that the right side was generally seen as more powerful/significant than the left. 1 Thus, people would rather lose their left eye and their left hand than their right. By mentioning the right hand, Jesus is saying that your most important and significant appendage is not nearly as important as making sure that you are not thrown into the fires of hell.
29 If your right eye causes you to sin, tear it out and throw it away. For it is better that you lose one of your members than that your whole body be thrown into hell.