The play within a play comes about because Prospero uses his magic to stage manage a drama on the island. This starts with him, through Ariel, creating the tempest that shipwrecks his enemies on the island. He then has Ariel scatter them around the island.
Prospero has Ariel inform Ferdinand that his father has drowned, which is not true, and makes sure Ferdinand sees Miranda, so he can fall in love. But Prospero also stage manages events so that Ferdinand can't win Miranda too quickly. He is the director of almost all (or at least much) that happens.
Prospero creates a dramatic banquet, and also stage-manages the denouement , where the various scattered shipwrecked souls are brought together and where they are forgiven their...
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