Football is a game of momentum and emotion and the home crowd helps with these and the home team seems to feed off the energy of the crowd. Not to mention, the home crowd can create problems with the visiting team verbally communicating---often, a visiting player did not hear a signal when a play blows up.
Everyone realizes that people perform better when performing in front of people that support them. Not to mention the fact that communication is easier between players and coaches when the home field fans are cooperative. If home field was not an advantage, more visiting teams would win, which is simply not true.
I think that when a football team is playing on their home field they have the power of persuasion on their side. To be able to hear their hometown fans cheering for them in such a loud roar, would get them pumped up and excited. Teams have been chanting and getting themselves worked up before games because, if you are in a mindset to win you will have a better chance.
The home field advantage can matter in football, though it is not the primary factor in any win or loss. When a team is on its home field they know the every in and out of the turf. They will not be surprised by any terrain matters, so they may have an advantage.