The crossover is the part of your driveway from the road up to your property boundary (ie they "cross over" the verge). Although the crossover is located on the verge which belongs to your local Council/Shire, it is usually up to each property owner to develop and maintain the crossover. In some areas there are rules about what you can use to construct your crossover or how much of your verge may be sealed - contact your local Shire or Council for more information.
Many Shires or Councils offer a small financial contribution towards the cost of installing a crossover, usually limited to one per property. Contact your local council for more information as every area is different.