Thou shalt not covet thy neighbour’s house, thou shalt not covet thy neighbour’s wife, nor his manservant, nor his maidservant, nor his ox, nor his ass, nor any thing that is thy neighbour’s. (Exodus 20:17)
To covet, in this sense, is to want something you can’t have. It can also be to want something simply because someone else has it and you don’t.
In a way, this is the beginning of the violation of all the other commandments. We start by coveting our neighbors property, and we end up stealing. We covet someone else’s (perhaps future) wife, and we end up committing adultery. We covet their life, and we end up killing them. We covet our parents, and we don’t honor them. We covet God, and we end up not worshiping Him.
We should never say in our heart that we want to be better than them for the sake of being better, nor that we want what they have simply because they have it.
I don’t think that greed is the same as coveting, although they are similar. Greed wants ever more, while covetousness simply wants what they have. Both are bad, although we are warned against coveting, not greed, in this commandment.
If we see our neighbor’s success, we should be happy that they are happy. If we want what they have, we figure out how to get it for ourselves. We are, after all, all creations of God, all equal partakers of the divine gift of life. We are also unique, special, different, each given their own talents and advantages, and each given their special challenges.
The point of life is not to look around and compare ourselves with each other. It is simply to find happiness. Happiness isn’t found in having more than your neighbor, it is found in satisfying the cravings of your own soul, the desire for peace, the desire for joy, the desire for good people who love you and whom you love, and the desire for simply spending your days on this earth in way that is pleasing to God and His divine principles and attributes.
Such a life cannot be had if you allow yourself to covet.