。
They arrived late because of the storm.
Literal
Storm [because-of-ため] they [topic-は] late-ly arrived.
遅れて is the te-form of 遅れる ('to be late'), functioning adverbially here to modify 着いた ('arrived') — essentially 'arrived in a late manner.' The te-form stacking a manner-verb onto a main verb is a core Japanese pattern for expressing 'doing X while/in a [manner] way.'