First some simple definitions. In our immune system, we have a number of different cell types. Of the mononuclear cells that circulate in the peripheral blood, there are at least two major kinds, the lymphocytes and the macrophages. But, a lymphocyte educated at Stanford will only recognize the Stanford antigen, and not an antigen studied by those lymphocytes that attended Cornell. It is also possible that the educated lymphocytes are not all that smart.
Macrophages are also mononuclear cells, but ones quite different than lymphocytes.
When they encounter foreign material, they eat it and then cover themselves with the regurgitated debris. But I promised to be simple. These are effectively messages that attract other cells and cause them to participate in the action. Some of the stuff that the macrophages make are free radicals. Free radicals include simple chemicals like hydrogen peroxide.