Specularity produces shiny highlights on surfaces.
It involves 3 attributes: the specular color and the shininess of the material, and the specular color of the light source.
glLightfv(GL_LIGHT0, GL_SPECULAR, [1, 1, 1, 1])
glMaterialfv(GL_FRONT, GL_SPECULAR, [1, 1, 1, 1])
glMaterialf(GL_FRONT, GL_SHININESS, 50)
A higher GL_SHININESS value produces smaller highlights.
To disable specularity, set the specular color to black ([0,0,0,0])