Fan points are simply Yahoo!'s way of saying fantasy points. You'll often find 'fan points' written beside the total number of points a player earned for a given week, or what they are projected to earn.
You may also find fan points per game, which is simply fantasy points per game. The total number of fantasy points for a given player may change depending on what scoring system your league runs. The fantasy points for a player listed on the homepage will be calculated using the basic scoring system.
Projected fantasy points are often calculated based on past performances of a player, especially how they are performing more recently. Sometimes these calculations may also take into account the over/under bet in Vegas.
Yahoo differentiates scoring for players based on the statistics you come across during a game. Quarterbacks accrue passing statistics more than anything else. A player can earn points for passing yards and passing touchdowns. They can also lose points for interceptions thrown.
This is a statistic that is accumulated by just about any player in today's NFL. When the sport first started, running back was the only position where players would get rushing yards. But now, quarterbacks and sometimes even receivers will be involved in a run play and get rushing yards. Players also can earn points when they get a rushing touchdown. They can also lose points if they fumble the football and it is recovered by the opposing team.
Just like rushing stats, running backs and wide receivers/tight ends are the main positions involved. Most leagues will award a player one point or ½ half point for catching a pass. As well, players get points for all the receiving yards they allot during the course of a game and points for the touchdowns they get in a game.