We aren't explicitly told why Lennie likes to pet soft things, but we can reasonably surmise that it is linked to his innocence. He is mentally a child, and softness is not only nice--isn't it to you?--but it soothes him. He likes stroking soft things.
In the opening scene, for example, George and Lennie are walking along when George asks him what he has in his pocket. Lennie says he has nothing in his pocket, and George says, "You got it in your hand." He discovers that Lennie is holding a mouse--a dead one. This disgusts George, so he takes the mouse and throws it to the other side of the pool, saying "What you want of a dead mouse, anyways?" Lennie replies: "I could pet it with my thumb while we walked along."
We see immediately that Lennie is so simple that he quickly forgets things. He has already forgotten what has happened in Weed (he stroked the dress of a girl because it was soft, for which they were driven out of town). The only things he remembers are that George is his friend, they plan to have a rabbit farm some day, and that he likes soft things.