Firing Arc is a projectile attribute referring to the path the projectile takes from the unit that fired it to the target the originating unit is attacking.
Firing Arc is important for a few reasons, most notably a low firing arc can reduce accuracy over rough terrain, and a high firing arc can cause a long delay from the time the projectile was fired until impact.
An extreme example of a low firing arc is the Rhino. While capable on flat terrain, the Rhino's shots frequently collide with terrain when on a hill or other non-flat surface.
An extreme example of high firing arc is the Stonager's nuke weapon. Despite possessing perfect accuracy geographically (the nuke will always land where targeted unless it is destroyed by an Anti-Nuke), the Stonager will often miss it's intended target (for example, an enemy ACU) because the intended target was able to move well outside the blast radius before impact.
Other examples of low firing arc include the Evensong and the Hunter. Other examples of units with high firing arc are the Lobo and the Aloha. The Majority of units possess something in between high and low firing arcs.