A "brink" is the edge of somethng high, like a cliff.

English speakers often use this word to talk about something bad or dangerous that almost happens. For example:

She was on the brink of death, but they were able to nurse her back to health.

The U.S. was on the brink of economic collapse.

Other things that something can be "on the brink" of include:

• on the brink of war
• on the brink of insanity
• on the brink of losing control
• on the brink of bankruptcy