The Site Arrow is an arrow located on the right side of every site card (on the bottom if you've rotated the site properly). This arrow is unused in 2-player 1v1 matches.
In multiplayer with 3 or more players, this arrow is used to determine which Shadow player plays the next site when the Free Peoples player moves. This keeps things nicely mixed up, rather than only one person playing all of their sites at everyone else's expense.From the Comprehensive Rules 4.0:
If your fellowship moves to a site that has not been played yet, one of the Shadow players must place a new site on the adventure path. (See moving your fellowship.) To determine which player, look at the site you are moving from. Each site has an arrow at the bottom center of the card. This indicates who is to play the new site, with » meaning the Shadow player to your right and « meaning the Shadow player to your left. In a two-player game, there is only one Shadow player at a time, so that player always plays the new site.