Cole was the mayor of Ember during the events of the first book. He is generally described as fat and greedy. As the generator starts to decay and the people of the city grow more scared, he gives speeches to motivate the citizens, although these speeches are usually less effective, since he uses an apparently faulty megaphone, which makes his speech hard to understand.
During the events of the first book, Lina Mayfleet first encounters the mayor on her first day as a messenger. After growing anxious while waiting to deliver a message to the mayor, Lina explores the building and soon finds herself on the roof, where she attracts much a attention. At this point, the guards come to take her away from the roof, and she is met by a mildly annoyed Mayor Cole, who soon dismisses her after hearing the message.
Later on, while exploring the Pipeworks while searching for a door out of the city, Doon Harrow and Lina encounter a locked tunnel, marked as "caved-in". They soon discover this is not the case, and find at the end of the tunnel a locked door. They hear a noise, and hide. Then, a figure walks past them. We later find out this is Looper, as in the book. They decide to call it a day. Yet on another expedition to the Pipeworks, they visit the same locked door, and discover that whoever is using the door left the key in the lock. Thinking it might lead out of Ember and compelled by curiosity, they open it, only to discover the mayor in a large room full of supplies like food and lightbulbs, apparently having decided to hole up in the underground room while the city starved and he used up his own personal stash, which could have helped the city a lot.
Later, during the beginning of the second book, it is revealed that during the evacuation of Ember, Cole's boat capsized, and he presumably perished, drowned in the river's current. He is mentioned no further in the storyline. In the movie, he was killed by the mole monster.