I saw a big teardrop falling from the corner of Koichi’s eye.
The kanji and the word are exactly the same. That means they share meanings as well. This refers to a literal edge, not a figurative one.
Since this word is made up of a single kanji, it probably uses the kun'yomi reading. You did not learn this reading, so here's a mnemonic to help you to remember:
If you're on edge, just eat some hash (はし) browns to feel better! And if you're going to the edge of the world, hash browns will probably help you make it there too. Hash browns are so useful!