Why does it conduct more before and after this minimum point?

Let me give you an example. Lets say that we have an amount of Ba(OH)2 compared to H2SO4. And let's say that the Ba(OH)2 dissociates as Ba+2 + 2 OH-. H2SO4 dissociates as 2 H+ + SO4-2. So, what happens here is that when the conductivity is at a minimum it means that stoichiometric amounts of Ba(OH)2 and H2SO4 are present and the only materials you can find there in the reaction vessel are H2O and BaSO4. That is why it conduct more before and after this minimum point