The moment just before something happens; on the verge or eve of an event (used to indicate 'just before' an action or occurrence).
出発の間際に電話がかかってきた。
I got a phone call just before departure.
試験の間際になって、急に不安になった。
Right before the exam, I suddenly became anxious.
彼は会議の開始間際に入室した。
He entered the room just before the meeting started.
The edge or verge; the near boundary — can refer to a physical edge or borderline in certain contexts.
川の間際まで下りて写真を撮った。
I went down to the riverbank and took photos right at the edge.
崖の間際まで近づかないでください。
Please don't approach the edge of the cliff.
店は閉店の間際でも客が並んでいた。
Even at the verge of closing, customers were lined up at the store.