The inclusions induce an ordering on the subtoposes of that makes them a lattice with a co-Heyting algebra structure i.e. the join operator has a left adjoint ‘subtraction’ operator.
(as every Grothendieck topos over ) is the classifying topos of some geometric theory and it can be shown that subtoposes of correspond precisely to deductively closed quotient theories of (cf. Caramello (2009), thm.3.6 p.15) i.e. passage to a subtopos corresponds to adding further geometric axioms to - localizing geometrically amounts to theory refinement logically.
F. Borceux, M. Korostenski, Open Localizations , JPAA 74 (1991) pp.229-238.