There is some element of surprise in the last line of "The Eagle." The eagle has been been standing still and watching in the other five lines of the poem. Then, suddenly, he falls into action.
"Like a thunderbolt he falls" in the last line is a simile, a comparison that uses the words like or as. Tennyson's speaker uses the simile of the eagle as a thunderbolt because it is a complex image that carries several ideas. First, a thunderbolt is very sudden, which would be similar to the action of an eagle suddenly falling on his prey. Second, a thunderbolt is an allusive image: it brings to mind powerful gods like Jupiter or Thor, who wielded thunderbolts. This communicates that the eagle is a powerful bird, sitting atop the world like a god in the heavens. Also, thunderbolts in various mythologies are depicted as weapons. The simile therefore suggests that the eagle is like a weapon, heading for its target in a powerful way.
This is a very short poem of only six lines, and Tennyson is trying to be as economical as possible in his word choices. Comparing the eagle to a thunderbolt is an elegant and compact way of conveying many ideas at once.