The chapter's most quoted verse, and the Hebrew verb is debated.
Quick answer
People sharpen each other the way blades do, and blades are sharpened by friction against something equally hard. The verse is about the contact, not about encouragement.
Read both lines
What usually gets lost in quotation is the mechanics. Iron is not sharpened by soft things, or by agreement, or by proximity. It is sharpened by another piece of iron, applied with pressure, and the process removes material. Whatever this verse is promising, it is not comfortable.
The second line is more specific than the popular reading allows. It is not that a man improves his friend generally; it is that he sharpens his countenance, his face, which in this book is where a person's bearing and readiness show. So the effect is visible. Something in how he carries himself is different after the encounter.
Why translations differ
The Hebrew verb is יָחַד and it appears twice, once in each line, with the NKJV supplying "sharpens" both times. The root's ordinary sense is to be joined or united, not to sharpen, and translators reach the sharpening sense either by reading a different but similarly spelled root or by taking the joining as the joining of blade to blade. Versions differ, and some render the second line quite differently. This expression is debated. What the entry rests on is not the verb but the picture, which every reading preserves: two hard things in contact, and something changed by it.
Related: Proverbs 27:6 · Proverbs 27:9 · Proverbs 13:20 · Proverbs 15:31
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.