Arda is the fictional world whose history is told in much of J.R.R. Tolkien’s legendarium.
In Tolkien’s mythology, Arda is the world created by Eru Ilúvatar and shaped through the actions of the Ainur. Middle-earth is a major region of Arda, not the name of the entire world. This distinction is important because many stories take place in lands beyond Middle-earth, including Valinor in the West.
The history of Arda changes dramatically across the Ages. Its geography is altered by major events such as the destruction of Beleriand and the downfall of Númenor. Tolkien’s later writings also describe changes in the world’s shape and the transition from an earlier mythological age toward the familiar world.
Valinor is a land within Aman, while Beleriand and Númenor are particular regions or realms from earlier periods. They are therefore related answers, but none names the complete world. Arda is the broad cosmological setting for the legendarium.