Politics is where things in the game revolve around the players' relationships to each other.
Politics can easily push aside other forms of strategy, as a player's fate is decided arbitrarily by who the other players choose to attack. "I'll use my dragon to destroy… umm…YOU!" It can also lead to unpleasantness, and accusations of unfairness.
Politics can be one of the most feelbad things in board gaming, if applied incorrectly, which it often is. Many games have aggressive, targeted elements thrown in, on top of a non-political game.
To remove politics, you can:
For very adversarial games, I like this answer best. It enables you to make the game for the player count it's best for, without forcing it to be something else.
In my gangster game, attacks hit all other players.
In my pirate game, you can only attack someone on the same space as you. You could technically travel to any player, but you'd need a logical reason to do so.
Make attacking about theft, not just beating down the opponent.
In my pirate game, you attack someone, in order to steal their cargo. Attacking just to hurt them would be far less satisfying.
Tack on a bonus to attacking, so a player will do it for their own benefit.
It's fine that players can choose who to attack. However, if the decision is completely arbitrary, other players can't plan around it. It's simply random and feelbad. Given the opportunity to attack a player arbitrarily, most experienced gamers will search for a reason to choose who to attack, and avoid accusations of unfairness. Attacking the winning player is the usual convention, as it tends to give the attacker the best chance of winning the game.
For less-civilised gamers, politics is an opportunity to hit someone for non-game reasons. The game devolves into a bizarre and unpleasant social metagame, about who likes who most.
Whatever your solution, it needs to make the choice of who to attack be based on more factors than just the whimsy of the player doing the attacking. Even if a player is the victim of such an attack, they'll be okay with it, as long as there was a good reason they were the target of the attack. Also, they will often be expecting the attack, which allows them to plan around it.
As with everything in games, a game should have lots of politics, or none. A game should be about politics, or without politics at all. Do not throw small political elements into a game that's largely not political. However, if players are bashing away at each other all game, and the game is about their relationships to one another, that's fine.
Games about politics tend to be the most basic and inane of all designs. Designers who know nothing about design constantly make "take that" games, where the players just play good cards on themselves, and arbitrarily play bad cards against other players. This is an extremely weak and overused format. Don't do it.