What, exactly, is the nature of the friendship between George and Lennie in Of Mice and Men? What makes it so unusual?

George looks out for Lennie, while Lennie provides companionship for George.

Although George and Lennie are not related, they each get something out of the relationship.  George looks out for Lennie, and he likes having someone there for him.  If George didn’t have Lennie, his life would be easier, but it would be lonely.

George complains about how difficult life is for him since he has to take care of Lennie all the time.

"Whatever we ain't got, that's what you want. God a'mighty, if I was alone I could live so easy. I could go get a job an' work, an' no trouble. No mess at all, and when the end of the month come I could take my fifty bucks and go into town and get whatever I want….” (Ch. 1)

However, despite this speech, George continues to go around with Lennie.  This is because despite the hassles Lennie causes, George would still rather have someone there than not.  George tells Slim it is “a lot nicer to go around with a guy you know.”  Slim is impressed that George and Lennie travel together.

"We kinda look after each other." He indicated Lennie with his thumb. "He ain't bright. Hell of a good worker, though. Hell of a nice fella, but he ain't bright. I've knew him for a long time." (Ch. 2)

Lennie is a hard worker, so George and Lennie can get jobs.  They can keep them too, as long as Lennie behaves himself. Sometimes Lennie gets into trouble without meaning to.  This is another reason why he needs George.  He looks to George for guidance, but when he gets in trouble George gets him out.  

George tells Slim that he used to tease Lennie out of frustration until he realized that Lennie would be loyal to him no matter what.  Lennie may be dumb, but that kind of loyalty means something to George.  He doesn't have the heart to be mean to him.  He yells at him sometimes, but he is never cruel.

Slim is impressed with Geroge and Lennie's relationship because most guys do not travel in pairs.  They look out for themselves and no one else.  They do not stay in one place very long, and it is a lonely and isolated life.  There is no consistency.  Having someone with you gives you something to count on.  Most guys have not found someone they can trust.  George and Lennie have found that.