Since Pres. Bush was president so recently, and because he was so controversial, it is not yet clear what he accomplished as president. Pro-Bush people will argue that he had many accomplishments while his detractors will argue that he had few or none.
In foreign policy, Bush is most closely connected to the War on Terror. His proponents argue that his policies have allowed the US to avoid any terrorist attacks since 9/11/2001. Bush proponents would also argue that progress in Iraq is due to Bush's policies.
In domestic policy, Bush's signature issue was tax cuts. The Bush tax cuts seem to have become permanent, which is something that conservatives would view as an accomplishment on his part. There is less consensus as to whether Bush's creation of the Medicare drug benefit was an accomplishment or a mistake.