Thunderbolt is essentially just a much more powerful (and expensive) version of Lightning Bolt, with added sound effects and screen shake.
Like most Lightning spells, it can be used to set off Lightning Runes from a safe distance.
It has much shorter range than the equivalent Incinerate and Icy Spear spells, but the fact that it is cast instantly instead of as a projectile makes it much easier to hit moving targets so long as they're within range.
Thunderbolt is very useful for fowling (Hawks, Bone Hawks, Felsaad Terns). As long as the birds aren't flying too high, they can be hit with only a little bit leading. Best to use where the fallen bird can be reached.