He commuted to work on a train from NYC to Connecticut and he fell asleep. He woke to find he was back in time to the 1880's and at a train stop for a town he had never heard of called Willoughby. He looked out the window and couldn't believe how peaceful the town looked. There were little kids going fishing with their cane poles and a band playing at the gazebo in the center of town. Everyone was smiling and laughing.
He woke to find he was back to the modern world again and part of the rat race. He tried desperately to find a town called Willoughby on the map but he couldn't. He fell asleep again while commuting and went to Willoughby a few more times but each time he was afraid to get off the train and interact with the people.
He began to have a nervous breakdown at work and decided to quit. He also decided that if he found himself back in Willoughby again, he was going to walk off the train to see what happens. It did happen and when he stepped off the train people were glad to see him and apparently knew who he was. He was loving it.
Then the next scene showed him dead near the train tracks and back to the current time. The conductor said the man was mumbling and then stepped off the train while it was moving. They figured he'd killed himself. Then at the end of the episode they show the man being placed into a hearse and when they close the doors to the back of the vehicle it read: "Willoughby Funeral Home." Gotta love "The Twilight Zone!"