Pure H2SO4 & dilute H2SO4

Because sulphuric acid is an electrolyte . When they are in aqueous state, they can conduct electricity.
Pure sulphuric acid = non - aqueous covalent compound, which does not contain free electrons .
DILUTE sulphuric acid = aqueous sulphuric acid, which contains free electrons.
If there are free electrons within the substance, it can conduct electricity.
This is why dilute sulphuric acid can conduct electricity but not pure sulphuric acid

It is because, dil H2SO4 is a electrolyte, it conducts electricity because there is moblie ions inside NOT free electron.
When Pure H2SO4(l) dissolve in water, H2SO4(aq) will form and show the properties of electrolyte.
Take sodium chloride which is an electrolyte as an example. originallly NaCl(s) cannot conduct electricity, however when it is put inside water, it exists as aqueous solution, moblie ions are formed and conduct electricity.
Electrolyte is compounds containing metal ions such as Na+ Mg2+ etc,
But acid is an exceptional case.

pure sulphuric acid does not contatin H+ ions and SO4 2- ions. Hence, it does not conduct electricity.

however, dilute sulphuric acid contains both ions above, hence, it can conduct electricity.