When we start something new, we perform Ganapati puja. That is usually the tradition. He is also called Vinaayaka, Ganaadhipati, Gajanana etc. He is called Ganaadhipati because he is the leader to some Ganaas. Ganaas are subordinates to God with some super powers. So, how did he become the leader to the Ganas?
When it was time to decide who will be the leader to these Ganas, both Ganesha and Kumara Swami were both thought to be eligible for being the leader. So, to decide who is the right person for the job, they were both given a task by Lord Shiva. Whoever goes around the world, takes bath in all the rivers of the world, visit all the temples and comes back first, will be the leader.
But, there is a problem. Ganesha travels around on a mouse and Kumara Swami travels on a peacock which is much faster. Ganesha is also slow to move and is obviously going to take a long time to go around the world compared to his brother Kumara Swami.
As soon as the task is given, Kumara Swami leaves immediately to finish it. Ganesha keeps thinking on how to achieve this impossible task. He then goes upto his parents and goes around them 3 times and takes their blessings.
While Kumara Swami is going around the world and visiting all the rivers, he always sees Ganesha leaving ahead of him. This makes him wonder how is that possible? By the time he gets back, Ganesha is already there waiting for him. Then he realizes what Ganesha had done.
So, respecting your parents and getting their blessings is equal to getting the blessings of all the Gods in the universe. Ganesha wins the task using his mind. He thinks clearly and realizes that he does not need to go around the world as long as he gets his parent’s blessings. Even though Kumara Swami had an advantage of going on a peacock, Ganesha does not panic.