Fast, expensive, and specialized in Air Combat, Fighters are situational units that don't see as much play as other units.
Fighters have one purpose: to destroy other Air units.
Fighters will outright destroy or severely cripple other Air units, with the exception of other Fighters, which they still do moderately high damage to.
They are also one of the only units capable of hitting a hidden Stealth, the only other unit being other Stealths. With their high movement and high damage output, Fighters can keep a very large area free from enemy Air units.
This power comes at a price, however; Fighters are completely incapable of attacking Land or Sea units.
Even with their high movement, Fighters cannot attack any units if their attack paths are blocked by a Land unit.
Because of their limited target selection and high cost, Fighters are uncommon units to see in a battle, typically only being built once an enemy starts building Stealths. Otherwise, Anti-Airs are quite capable of doing high amounts of damage to air units, for a much lower cost.
Typically, your enemy would only build fighters if you are using Stealths. Even if a Fighter can hit a hidden stealth, it still needs to have another unit adjacent to your Stealth to be able to attack it.
When using Stealths against Fighters, the best course of action is to keep the opponent guessing where the Stealth will strike next, picking targets that the Fighter cannot reach effectively or safely. Over time, the Stealth will prove to be more valuable than the Fighter.
With other Air units, the only thing that can be done is to avoid the Fighter where possible, which can prove difficult thanks to its high movement range. Surrounding your own Air units with Land units will prevent the Fighter from being able to reach them, keeping them safe.