the edge of a steep place
"The hikers froze as they stood on the very brink of the cliff, looking down at the dizzying drop below them."
The edge, margin, or border of a steep place, as of a precipice; a bank or edge.
"The hiker stood on the brink of the cliff and looked down at the rushing river far below."
A surname.
"The local history club invited Mr. Brink to speak about his family's early settlement in the valley."