。
My decision to study abroad surprised my parents.
Literal
Study-abroad [volitional-しよう] [quotative-という] my determination [topic-は] parents [object-を] surprised.
留学しようという (the intention to study abroad) uses the volitional form + という to package a planned action as a noun-modifying clause. 驚かせた is the causative of 驚く — 'caused to be surprised' — putting agency on the decision itself rather than on the parents' reaction.