Extensive variables depend on the amount of material. These are a material's properties such as mass and volume.
Intensive variables are independent of the amount of material. These are either properties like temperature or others that combine, or are the ratio of, two extensive variables like density (mass/volume) or molar volume (volume/mole).
So our state functions can be either intensive or extensive.
We'll deal a lot with energy changes and it is important to keep track of when we are talking about extensive changes. These are usually very particular questions about specific amounts of a substance: how many joules of heat are released by reacting 10 g of carbon with an excess of oxygen gas? This clearly depends on "the amount of stuff" and will be a certain number of joules (J). The answer for 10 g will be different than for 5 micrograms. Alternatively, we could be talking of intensive energies. How many joules of heat are consumed for every mole of ice that melts? Now I want to know how much energy per mole? The question doesn't ask about a specific amount and will have an answer that is in joules per mole (J mol-1).