Generally speaking, the war aims of the Axis countries were quite similar to one another and the war aims of all the Allied countries were similar to one another. Therefore, I will discuss the Axis and Allies, respectively, as if each were one country.
The Axis countries wanted to gain more land. All of the countries of the Axis felt that they deserved and needed more territory so that they could have more space to live in and so they could have more resources to use to enrich themselves. They felt that they deserved empires like those held by the Allied powers. It was generally for this reason that they started the war.
The Allied powers were really just trying to prevent the Axis from winning. The Allies did not aim to take any territory for themselves. Instead, they were simply fighting to defend themselves and to push the Axis powers back to where all they had was their home countries.
For the Axis, then, this was an aggressive war meant to take territory. For the Allies, it was a defensive war meant to restore the status quo as it had been before the Axis countries started trying to expand in the 1930s.