Non-self
One of the fundamental teachings of Buddhism is that our sense of individuality is delusional. The Buddha taught that we aren't really individual beings in the way that we tend to think. We are really just part of everything else, like how waves are part of the ocean. A wave can be described as an individual, but it isn't really separate from the rest of the ocean. The Buddha taught that what we think of as our self is actually not an individual being, but a combination of things. He called these the five aggregates. They are: physical form, consciousness, feelings, perceptions, and mental habits. If we are just a collection of things, like parts of a car, then our self is less significant than we think it is.
So, what are the implications of this? Well, feelings of greed and jealousy become insignificant if we aren't so focused on ourselves. I think everyone agrees that the world would be a better place with less selfishness. Recognizing ourselves as part of a context rather than thinking we are some separate independent being can go a long way toward fixing many of the problems in the world. If we recognize others as ourselves then we are certainly less likely to harm them. It can make us want to help them instead. And ultimately helping others is really important in Buddhism.