にあたって means 'at the time of' or 'on the occasion of', and it sets a formal, ceremonial tone. You use it when you want to say something like 'upon starting this project, I want to thank everyone' or 'at the start of the ceremony, let us observe a moment of silence'. It often appears in speeches, official announcements, and written notices, so it sounds stiff in casual conversation.

Because it marks an important juncture, the verb or noun before it is usually something like 卒業 (graduation), 出発 (departure), 開始 (start), or 実施 (implementation). The phrase that follows typically expresses a resolution, a request, or an action taken in light of that occasion. For example, 実施にあたって is a set phrase meaning 'in implementing' or 'for the implementation', and you often hear it in business or administrative contexts.