Ichigo will come to realise that he's an avatar of the King of Soul Society, who wished to experience the ordinary world, and so poured his soul into a human body. This is why Ichigo's spirit pressure is constantly overflowing. Isshin, the Captain of the Royal Guard, became his "dad", so that he could better protect him. Ichigo of course has no memories of being the king, so kicking the king around in the house is Isshin's idea of a joke.
Eventually, Ichigo goes to the dimension of the King and understands everything after seeing the empty throne room. As a result, he becomes the most powerful character in Bleach. He kills an army of 1000 Menos Grande with a single Getsuga Tensho Omnislash, and proceeds to battle the number 1 espada with bare hands.
It turns out it's all been part of a master plan to lure out the strongest villains in Hueco Mexico and kill them. Aizen was only acting out the role the King gave him (hundred-something years ago), in order to manipulate the hollows. After everything is over, Aizen resumes his position in the Gotei 13 and becomes the Captain General in the place of Yamamoto, who was killed by the first espada.
In the last scene, King Ichigo tells final farewells to his old comrades and thanks them for the happy life he had on Earth, before ascending to the Heaven's Throne. The End.