The Story of Gajendra (The king who was transformed into an elephant) has a deeper significance. In this story, Gajendra enters a lake and plays with his friends when he is trapped by a crocodile. He tries to free himself but is unsuccessful. None of his friends are able to help him. The elephant surrendered to God. God alone was able to rescue him.
The significance in real life is - all of us (humans) are like Gajendra. The lake that he entered is like this world, where we live with other people (friends, family etc.). The grip of the crocodile symbolizes the calamities and troubles that we face.
The takeaway from this story is that - while we live in this world with our family, friends and society, when we face problems, the only one who can rescue us is God.