。
We postponed our departure because of the storm.
Literal
Storm [because-of-に-ために] departure [object-を] postpone-did.
延期する ('to postpone / defer') is a formal suru-verb contrasting with everyday synonyms like 遅らせる. The subject is omitted — the sentence doesn't say who postponed what, and Japanese leaves that entirely to context. A learner should note how the bare 延期した stands as a complete predicate.