Something that's unbridgeable is hopeless — it can't be solved or made smaller, like the sometimes unbridgeable gap between two rival political parties.
You'll almost always find this adjective accompanied by words like gap or divide. You might describe the unbridgeable communication gap between you and your parents or an unbridgeable difference between how much houses cost in a town and the income of most residents. A river that's too wild or prone to flooding for a bridge to cross it is quite literally unbridgeable, from the verb bridge, "build a bridge over."