？
What on earth drove them to take such action?
Literal
One-body what [subject-が] them [obj-を] that-kind-of [attr-な] action [to-に] drove-up-[past-た] [question-のか]?
A rhetorical question in formal register. 一体 is the emphatic adverb 'on earth, in the world' used to intensify interrogatives ('what on earth,' 'why ever'). 駆り立てる ('to drive, to urge, to compel') is a compound verb: 駆る ('to urge, to ride') + 立てる ('to stand up, to cause to rise'). ~のか at the end is explanatory の + interrogative か, softening a blunt question into a reflective 'why is it that...?' The whole sentence has the rhetorical heft of an editorial or narrative narrator.