Self describes agents that are recognized by the immune system of an organism as being part of that organism by the presence of marker molecules known as MHC markers. Non-self describes agents that are not recognized by the immune system as being part of the organisms due to the presence of receptors that identify the agent as non-self.
The above image shows this in a pictured form; with the self-receptors being shown as a grey color and the non-self receptors being of a green color. The specific shape of the self-receptors will only bind with antigens from cells with the complimentary shape that will fit into that receptor. While cells that do not have the specific self-antigens are recognized as non-self