This analogy is from the Shrimad Bhagvat Geeta. Lets see this in this way, our body is not who we are, its just a vehicle we are travelling in, we are on this cosmic journey and loberation is our destination.
Our sense organs are just like horses, they go wherever they want if we keep our mind free. So our mind is the rein, if rein is free, horses will loose the direction, and every horse will try to go in its own direction.
So to control our mind we do have intellect and yes intellect works as charioteer, who keeps the rein in his hands and keeps control over it and ultimately on horses. In the same way we should control our mind using our intellect.
And now comes the owner of the chariot, we are not our body we are our soul and thats the owner of our body.