Graphite is a mineral whose molecular structure is made up of carbon atoms. 

A carbon atom can bind up to 4 other atoms around it (it has 4 electrons in its outer-most shell which it can share with other atoms to form bonds).

However in graphite each carbon atom only bonds to 3 others around it- this means there is an electron spare which becomes 'delocalised'.

This means that it is donated to form a common pool of electrons which can flow through the molecule carrying charge and so conducting electricity.