This verse can be broken down into two sections: "He heals the brokenhearted..." and "...and binds up their wounds."
"He heals the brokenhearted..." Psalm 34:18 uses a similar language, "The Lord is near to the brokenhearted..." God knows the righteous - his eyes see us, his ears hear us, He Himself is near to us, and He rescues us.
"...and binds up their wounds" We are dependent upon the healing from Christ. Like I mentioned yesterday when we talked about being unable to search our soul ourselves to treat the root cause of our sin, we see further proof here that we are unable to spiritually heal ourselves. Only through faith in Jesus are healed through His sacrifice.
This simple 9-word verse is extremely powerful and comforting as a believer. The Lord is not only a builder, but a healer. Christ heals all by his blood, stripes, and wounds even though we do not deserve it.
Many misinterpret and take this verse (out of context) to mean that those who believe do not have fewer troubles. This is not what we're being told here by the Psalmist whatsoever. Nowhere in the Bible are we promised an easier life by believing in Jesus. Look at his closest followers, one died a natural death at an old age (even though he was in exile on Patmos).
We're told in John 15:18 by Jesus, "If the world hates you, know that it has hated me before it hated you."
Jesus heals the brokenhearted. Being a Christian isn't easy, but the joy of having God by our side as we go through life is immeasurable.
Sources:
Gill, John. "Commentary on Psalms 147:3". "The New John Gill Exposition of the Entire Bible". https:https://www.studylight.org/commentaries/geb/psalms-147.html. 1999.