Widely quoted, and usually as a verse about God inspecting you. The Hebrew word for "inner depths" is literally* rooms of the belly, *and it returns three verses later.
Quick answer
God gave a person an interior light. The verse is about the capacity for self-knowledge, and the lamp belongs to the man.
Read both lines
Grammar decides this one. The lamp is the spirit of a man, which the verse then says belongs to the LORD, so the picture is of something given rather than something aimed. The word in the first line is neshamah, breath, the word used when God breathes into the man in Genesis, and choosing it here is a claim about origin. Then the searching happens in the rooms of the belly, the Hebrew idiom for a person's innermost parts. So the sentence describes a lamp carried through the interior of the house it belongs to. That capacity is real, it is a gift, and it is the reason a person can know things about himself that no one else can reach.
What it does not mean
This is not a verse about divine surveillance, and it is often preached as one, with God holding the flashlight and the reader as the room being searched. The grammar does not support that and the pastoral result of it is unhappy: a Christian taught to read this verse that way is invited into permanent self-examination, checking rooms, waiting to be found out. Scripture does teach that God knows the heart, at 15:11 and elsewhere, and this verse is not where that is taught. Nor is the lamp a diagnostic tool for other people. Paul draws the natural line: "what man knows the things of a man except the spirit of the man which is in him?" (1 Corinthians 2:11). A person's interior is lit from inside, which is the reason nobody else gets to narrate it for them.
Related: 1 Corinthians 2:11 · Proverbs 20:12 · Proverbs 15:11 · Proverbs 20:30
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.