His name is Lennie. He is large, tall, and muscular looking. But, he has some mental illness that makes him act like a child. Luckily he has George to help him.
This is George and Lennie. They have a bond like brotherhood/fatherhood. George felt the responsibility to look after him, so Lennie would not get into trouble.
He was attracted to the girl's dress, so he touched her because he is attracted to soft things. But, the girl said he was trying to rape her, so they had to go on the run. They left quickly looking for work at another farm, and they had to walk for so long.
Throughout the story when they were going to the next farm you can see all the responsability George has over Lennie.
Is just a mouse and I want to pet it.
Yeah but you killed the mouse, for petting it too hard. Throw it away we are about to get to the new farm.
They had made it to the new farm and they had gotten the job. Weeks later something bad had happened Lennie got out of control and strangled a women but he didn't know what he was doing because he had thoughts of child. He just wanted to play with her soft hair.
Because of the incident about the girl that Lenni killed, they wanted to kill him now. The thing is they would've killed him but also, make him suffer and George didn't want that to happen, so he had to shoot him instead before they got to him.