The Hebrew carries a scribal variant that reverses the verse's meaning.
Quick answer
A curse with nothing behind it has nowhere to land. It stays in the air like a bird that will not settle.
Read both lines
The image is precise. Small birds in flight do not perch on you; they pass, and the eye follows them out of sight. That is what the verse says an undeserved curse does, and the comfort in it is real for anyone who has been on the receiving end of one.
Why translations differ
The received text preserves two readings of one short word. The written consonants give לֹא, "not," producing "shall not come," which is what the NKJV follows. The reading tradition gives לוֹ, "to him," producing "shall come to him," meaning back to the one who spoke it. The two readings are pronounced identically and point in different directions, one saying the curse lands nowhere and the other saying it lands on the curser. This expression is debated. Both readings agree on the thing that matters pastorally, which is that the person cursed without cause is not the one it settles on.
Related: Proverbs 26:27 · Numbers 23:8 · Proverbs 3:33
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.