Polybolos are a siege unit and variant of the Ballistae (Unit) in Classical Age. They have great attack strength for a Classical unit but have weak defence and are extremely slow, and are inefficient compared to every other artillery unit.
In reality Polyboli are something of an automatic version of the ballista, outfitted with a mechanism powered by a flat link chain (which were proportedly invented by Leonardo Da Vinci himself) which reloaded the machine for faster firing.
They are largely useless in almost every situation where the units are already trained; their attack power is less efficient per gold upkeep (which is limited by settlements, rather than acquirable on tiles) than the Ballistae or the Scorpio , and both are as accessible in tech. These units are also much faster than the Polybolos and can be used on attack as well as when holding a position.
Their low defense doesn't affect their survivability much - the extra point is largely useless as even a small (under 100) group of infantry could massacre hundreds of artillery pieces in one wave.
However, in a pinch, their their cheaper cost and quick training time means that these can be quickly constructed as defensive entrenchments/emplacements within the city, and even a few extra of these on hand will hugely affect any barbarians raid on your towns. Providing a standing garrison of infantry with back up, your defence will be much more formidable, eliminating enemy units before they can engage.