Quick answer
The righteous man's hope matures into joy; the wicked man's expectation dies before delivery. Both men are waiting for something. The proverb is about which kind of waiting has a future.
Read both lines
Both lines are about anticipation, and the Hebrew words for "hope" and "expectation" are close kin; the difference is entirely in whose they are and where they lead. The hope of the righteous "will be gladness": it arrives, it ripens, and the waiting turns out to have been the early stage of a joy. Hope anchored in what God upholds is not wishful thinking; it is patience with a delivery date.
The expectation of the wicked "will perish," and the verb is the one used for dying. His expectation was alive, vivid, confidently held, the scheme's payoff, the fraud's clean escape, and it dies, because it was staked on things that do not hold. The proverb recurs at 11:7 with the sharpest edge: when a wicked man dies, his expectation perishes with him. The question is never whether you hope. Everyone at every moment is expecting something. The question is whether the thing your hope is tied to can bear the weight of a future.
From this side of the cross
Hope in Scripture is not optimism about outcomes; it is confidence in a person. Which is why Hebrews calls hope an anchor and Paul calls it a helmet, and why the hope of the righteous survives even the days when nothing else does.
Related: Proverbs 11:7 · Proverbs 13:12 · Hebrews 6:19 · 1 Thessalonians 5:8
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.