In Context:

Matthew 5:27-30
27 “You have heard that it was said, ‘You shall not commit adultery.’ 28 But I say to you that everyone who looks at a woman with lustful intent has already committed adultery with her in his heart. 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. 30 And if your right hand causes you to sin, cut it off and throw it away. For it is better that you lose one of your members than that your whole body go into hell.

This is a literal translation of what Christ said.

But now for the meaning...Lust is a problem that isn't easily corrected on our own because it is both visual and emotionally compelling. If, key word, IF we can't control our lusts of the flesh and IF we go on down that road (and stay on that road) of sexual immorality then it would indeed be better, eternally speaking, if we could not see the objects of our lust or touch the objects of our lust.

This is similar to saying if we have hatred in our heart for our brothers, then it is really the same as murder. It is all about the heart issues and our proclivity to sin and repeat our sins even when we know better.

The reason we know that this is a warning to us and not a command to dismember ourselves is the obvious...what about the left eye and left hand?? The right side is the noble side, the honored side--and this has been used throughout history. So to pluck out the right eye or right hand was one of those shocking statements by Christ to wake up his audience (there with him and us today reading his words) to come to the understanding that lust of the flesh has serious consequences and we would be wise to turn away, repent and lean of Christ for help navigating the world full of desires of the flesh.