Kaneda's Bike
The bike distinguishes Kaneda from his friend Tetsuo. It is an early symbol of the difference they have in strength and the reason why Kaneda is the gang leader. It is easy to see that the bike plays a vital role as it is portrayed on the cover of the movie.
Tetsuo's Powers
Tetsuo's psychic powers also work as a symbol, as they are discovered because he is trying to impress his friend Kaneda. He gains them when he crashes chasing a biker from the clown gang, and they progress and develop throughout the movie. They can also be seen as his human potential that the government tries to misuse.
The Government
The government experiments on people and uses their powers for their own gain. It symbolizes the evil in human nature, and how the greed for power is stronger than even the fear of consequences.
Kaneda and Tetsuo's Friendship
The development of Tetsuo and Kaneda's friendship goes through different stages—from leader and student to vengeance and then to sacrifice. This works as an allegory and shows the true meaning of friendship and how it can transcend any obstacle.
Tetsuo Becoming a God
The power Tetsuo has and how it evolves into becoming a divine power has a deeper meaning. Instead of using his power like Akira did to destroy old Tokyo, Tetsuo uses it to create another universe where he is god. This shows how human beings can create their own fate and how vital it is to have people around you that you can rely on. There are two sides to every coin.