It started on 4chan with the 4chan Gold meme. Users would joke about a non-existent premium subscription that unlocked exclusive content. Reddit went ahead and actually implemented that idea, complete with the /r/lounge subreddit (available only to users with Reddit Gold).
Reddit users created Reddit Silver as another meme, indicating that a post was valuable (but not worth spending real money for Reddit Gold). Then reddit implemented that later on.
From my recollection gold came first, silver was a image macro meme to be pasted as a poor man's gold, and then the expanded rewards system came.