He is the uncle of Digory Kirke as well as a self-proclaimed magician. Andrew ends up also being one of the first humans to ever set foot into Narnia, witnessing how Narnia was created by Aslan.
In The Magician's Nephew
Andrew was born to the Ketterley family in 1840. Having squandered his family fortune on extravagances, he was forced to move in with his sister Letty. He had a godmother who was known as Mrs. Lefay whom he was not allowed to see because she was viewed as insane by the other family members. In fact, she claimed that she was a fairy and that she knew the existence of other worlds.
On her deathbed, Andrew was called to visit his godmother before she expired. She gave him a magical box and made him promise to burn it in a ceremony. Andrew didn't keep his promised, and he set out on a long career in magic.
Knowing that the box came by the means of magical origin, he desired to know how to use the contents in the box. He eventually discovered that the box came from Atlantis, and that there was dust that came from another world inside of it. In the summer of 1900, Andrew performed his first successful experiment with the dust, from the dust, he created several rings and they were used to send guinea pigs into other worlds. After this experiment, he sought human subjects for his experiments.
He found that help in the form of his nephew Digory Kirke and his friend Polly Plummer. After locking them in his study, he manipulated Polly into taking a yellow ring (which would take her into another world), but not a green one (which would take her back to Earth). He then made a compromise with his nephew: Leave his friend to an unknown fate in the other world, or go to the other world to get her back. Diggory was forced to obey him.
When he returned from the other world, he unwittingly brought Queen Jadis with him back to Earth. Jadis is angered to find the magician who sent Diggory is only a common man instead of a great ruler. She decides to make Andrew her slave and orders him to help her conquer Earth. Andrew complies, under the delusion that she will fall in love with him. Attempting to entertain her, Jadis causes chaos in London stealing jewels and a cab horse. When Jadis was fighting with the police, Digory manages to drag Jadis back into the otherworld. Polly, Uncle Andrew, the stolen cabhorse named Strawberry and Frank, its owner were all dragged into the otherworld as well. Instead of Jadis' homeworld, they all went to a seemingly void world. It is then that they saw the Great Lion Aslan himself creating Narnia. Uncle Andrew, however, was afraid of Aslan's power, and managed to convince himself that Aslan was just an ordinary lion. By closing his mind so hard, Andrew made himself incapable of hearing Aslan's voice, or any of the other talking animals of Narnia.
Andrew instantly made plans to exploit the new world after seeing a lamppost grow from a piece of iron dropped into the ground, thinking he could get rich growing ships and trains the same way. When talking animals came after him out of curiosity, he attempted to run, only to be captured. Believing him to be some strange possibly evil creature, the animals kept him prisoner (they were unable to understand him just as he could not understand them). He was then put into a cage by a few of the Talking Animals, and he was named Brandy (since he said that word so often). He is later presented to Aslan. Since Aslan was unable to speak to Andrew, he put the old man to sleep and made him forget everything that he had experienced. He and his nephew, as well as Polly were sent back to Earth. Jadis was banished to the Northern part of Narnia by Aslan, and the owner of the cabhorse became the first king of Narnia. His horse, Strawberry, also became the first pegasus in Narnia.
Digory and Polly made sure to bury all of Andrew's magic rings. When Andrew grew older, he gave up on his study on magic and moved in with his sister. He learned his lesson and became nicer in his old age.
Uncle Andrew was originally a man who sought recognition for himself, and thought he was greater than he truly was. He didn't think it was wrong to hurt other people in order for his dreams of greatness to happen. He was originally very selfish and cruel. For example, he talked down to his nephew about wanting his mother to be cured of her illness and he also had no second thoughts about sending a young girl into another world and leaving her there to an unknown fate. He considered anyone else who wasn't superior to him to be below him and groveled in the sight of anyone he considered superior to himself such as when he met Jadis. He also believed that he was above the moral codes since he was a magician himself. He was also rather cowardly and would drink when threatened. He would be very hard to use during times of need because of this.
He is also mentioned as being very lazy, never having done any work, and wasted his money on brandy and cigars. He was very vain, as well as foolish; on meeting Jadis, he managed to delude himself that she would fall in love with him. His only real interests are money and power. On arriving in the newly-created Narnia he is uninterested in anything, except the possibility of becoming rich and famous from the new country.
His selfish personality is what shuts him off from Aslan's influence. Since he refused to hear the power or the message of Aslan, he became unable to hear his voice, only animal sounds.
However, like it is mentioned above, he later became kinder when he became an old man, and he gave up on his obsession with magic.