Psalm 4:8 (or Psalm 4:9 in some versions, depending on the numbering) is a powerful statement of trust and dependence on God. Let's break down what it means:

"In peace I will both lay myself down and sleep": This speaks to a sense of tranquility and confidence. The speaker is able to rest and sleep peacefully, free from anxiety and fear. "Lay myself down" implies a deliberate act of resting, a conscious decision to surrender to sleep.

"for you, Yahweh alone": This highlights the source of the speaker's peace. "Yahweh" is the personal name of God in the Hebrew Bible. The phrase "alone" emphasizes that it is only through God that this peace is found. There are no other sources or conditions necessary for this tranquility.

"make me live in safety": This emphasizes God's protective power. It's not just about feeling safe, but actually being safe because of God's intervention and care. "Live in safety" implies a continuous state of security, not just a temporary feeling.

Therefore, the verse as a whole means:

The speaker is expressing a deep trust in God, allowing them to rest peacefully and without fear. The peace and safety they experience are not self-generated or dependent on external circumstances, but are gifts from God alone. They recognize that God is their protector and provider, ensuring their well-being even during sleep, a vulnerable state.

In essence, the verse conveys:

Trust in God's protection: The speaker trusts God to guard them and keep them safe.
Peace of mind: This trust results in a deep sense of peace, allowing them to rest without worry.
Dependence on God: The speaker recognizes that their safety and well-being depend entirely on God's grace.
Acknowledgement of God's sovereignty: "Yahweh alone" underscores the belief that God is the ultimate source of security and peace.

This verse is often used as a prayer before sleep, acknowledging God's protective presence and surrendering any anxieties to Him.