Here are some ways it's used:
* "The company was already struggling, and this latest setback pushed them over the brink." This means the company was already in a difficult situation, and the new problem made it impossible for them to recover.
* "He was on the edge of a nervous breakdown, and the news of his wife's illness pushed him over the brink." This suggests he was already close to a mental breakdown, and the news was the final straw.
* "The country's economy is on the brink of collapse." This means the economy is extremely weak and close to failing.
The "brink" is often used metaphorically to describe a dangerous edge or a point of no return. "Over the brink" suggests that something has gone too far, and there is no going back.