Autoimmunity and central tolerance
There can be many responses. They are important for alloimmunity (so by transfusion, transplantation, etc...), for recognizing pathogens, cancer, virus, etc... By T cell activation, the regulator T cells recognize these antigens as self, and prevent the autoimmune reaction.

I guess they were thinking on MHC1 and MHC2. MHC1 shows the inside of the cells, so e.g. by viral infection or cancer non-self oligopeptides (from degraded proteins) bind to MHC1. These non-self antigens are recognized by CD8+ T cells, which destroy the affected cells. MHC2 is used by APCs to present possible pathogens to CD4+ T cells in a similar way.