Meaning: This sentence expresses a wish for someone to have a pleasant and restful sleep.
Choice of Words: Sweet dreams are pleasant thoughts or images that come to mind while sleeping. Peaceful sleep is a state of rest without disturbance.
Alternative Expressions
May your dreams be sweet and your sleep be peaceful.
Meaning: This means the same as the first sentence, but it's a bit more polite and formal. It's like saying, I hope you have a nice dream and sleep well tonight, and I wish for your dreams to be sweet and your sleep to be peaceful.
Choice of Words:May is a modal verb that expresses a wish or hope, your is a possessive adjective that shows ownership, and be is a linking verb that connects the subject to a complement. When you put them together, "May your dreams be sweet and your sleep be peaceful" is a more formal way of expressing the same wish as in the first sentence.