Ballistics improves the accuracy of all ranged units by enabling them to hit moving targets more precisely. It can only be researched from the Government Center and is needed to develop the technology that upgrades Guard Towers to Ballista Towers. However, the only unit that is precise without researching this technology is the Mirror Tower.
The "improved accuracy" works by making an archer/siege unit/warship fire at where a unit is going to be (assuming they continue moving in the same way) rather than where they are. So if an archer tries to fire at a cavalry unit moving in a straight line past him where each shot would ordinarily miss, each shot would hit instead. This is particularly useful against the enemy AI.