It stems from being in your home city. Not having to travel. Playing in the stadium you’re used to. Sleeping in your own bed that week. Fans will be much louder and on your side as well.

The fields my be the same dimensions, but they're not the same. It's your field, your stadium, your livery, your equipment, your dressing rooms, and mostly your fan base. Also, you didn't have to travel to be here. There could be other factors, too, like you being used to the weather or other conditions.

Fans. Noise level can have a huge influence. If you can’t hear communication/teamwork becomes a lot more difficult.

Being in your hometown. Not having to travel to a different city for a game. No time zone difference. Eating local foods. Local fans rooting for you.

The crowd impact the game. Both for the players on the field and the referees making important calls.

It's basically like fighting and defending your turf, house, grounds whatever. People get a little more defensive about their ground/ property taken from them. I understand your confusion, usually it relates to warfare. Where an invasive country comes into another. People that live their,grew up there, know the territory better than the invasion army. Therefore homefeild has advantage. People just view football as war apparently and think same situations apply.

When the home team is on offense, the crowd will be quiet as church mice before every play, so that players can hear play calls. Conversely, when the visiting team is on offense, the crowd will scream their heads off.

its like going to your favorite closest place to have a lunch at, you know the staff, employees, menu, offers, they know you versus going out eating driving to another city to a different place

It’s all in the mind. You get extra support from your home fans that make for a more conducive environment for winning

When you have a home game you get the following:

• You spend the night in your own bed. And you can spend time with your family
• You can relax and drive yourself to the the arena at your own leisure.
• Staff and teams are familiar with the souroundings.
• You are better supported by the extended team staff.
• Home locker rooms and facilities are well staffed and emanates are everywhere.
• You will have the support from the home fans.

when you are traveling team.

• You usually need to travel the day before, sometimes two days before. Planes, trains, buses.
• You are spending a night in a hotel in places you are unfamiliar with..
• You are on a strict schedule because you are traveling as a team.
• you are getting to the stadium where you might not know where everything is.
• Your locker room is likely the bare minimum the home team needs to provide to you.
• you have to deal with a hostile crowd.

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A funny story about this was when teams came to play the Boston Celtics or Bruins at the Boston garden. The Boston garden was a dumb, but the visitor locker rooms were apparently disgusting. Mouse and rat traps, filthy and cold. But as the legend goes Boston Garden staff would aways sabotage the hot-water tank so visiting teams had to either have a cold shower or leave the stadium gross and sweaty. And in the middle of a Boston winter that is bad.

Also, in sports like NFL football or European Soccer/football teams usually travel for an away game. Then come straight back home. The follow week they will host.

in sports like Baseball, Hockey and Basketball teams usually go on road-tips where they play at several away stadiums in a row traveling from city to city. Sometimes playing back to back nights. Sometimes a team will have a game that will end at 10pm and they will be going straight to the airport to get the next city.

doing this for days and days on end can be EXHAUSTING when you are playing a rested home team with players that got to sleep in their own bed and eat a home cooked meal.

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In American football stadiums can be loud when the visiting team is trying to communicate. Depending on the city they will also throw batteries and hit Santa Claus with snowballs while eating horse shit to celebrate victories. The Oakland Raiders fans used to stab each other.

If you mean handegg the fields MAY be roughly the same since they’re synthetic but in real football the fields are not even the same size, let alone the ground itself. The grass is cut to different length, the substrate may be softer or harder, there may be large patches of grass missing… the list goes on and on.

Others have mentioned a long list of other factors that apply to any sport, but there’s also different lighting, and reference points that you acquired after playing in the same arena many times.