This is the first Military Policy with concrete battlefield effects: it enhances your cities' battle strength. However, note that the Policy applies only to cities which have Defenses (that is, at least Ancient Walls)! It has two different modifiers: the first works for defense only (that is, whenever the city is attacked, whether in melee or from a distance), while the second only applies to the city's ranged attack, effectively increasing its damage. In any case the Policy is only useful if you expect city combat, and will raise your cities' strength substantially, above the maximum for your current technical level...again, if they have Defenses only!
Bastions is a great Policy to use whenever you are on the receiving end of a surprise declaration of war. Typically this will happen after Turn 50, but sometimes aggressive neighbors may decide to rush you even before that - in this case, you'll be unable to use Bastions because there's no way you will have developed Defensive Tactics already. Assuming you do have Bastions, slot it, pull back your forces to your nearest frontier city, try to build Ancient Walls there (if you haven't already), and then surprise the surprise invader by crushing his army!
Bastions may be used through the early and middle game to defend against invasions, especially if you're focusing on different aspects of the game. If you have a strong army, the AI will hesitate to attack anyway, and may prefer a more tactical battle on neutral ground - in such case you won't have use for Bastions. And the Policy becomes obsolete in modern times anyway.
Civilopedia entry Edit
A bastion is an angular bulwark projecting out from a fortified wall, usually with two faces and two flanks; from the flanks missile fire could be directed along the wall against attackers that would otherwise be screened from above. Although more common in the Middle Ages, early examples can be found that were constructed during the Roman Empire. The Romans fortified their cities with massive, mortar-bound stone walls, and later – when those annoying barbarians started pushing past the borders – added bastions to several of these (such as the Aurelian walls of Rome and Theodosian walls of Constantinople).