Thou preparest a table before me in the presence of mine enemies: thou anointest my head with oil; my cup runneth over.
Some readers consider lines 5 and 6 to be the second part of the psalm because it's thematically different.
The metaphor of the shepherd completely disappears now.
The line describes how God lays out a banquet for the speaker, even when his enemies are nearby.
What is the role of the enemies, do you think? Has God made peace between the speaker and his enemies, and now they're sitting down for a meal together? Or do the enemies merely symbolize danger, in the presence of which the speaker is still safe and able to enjoy a luxurious banquet?
The whole of the poem is highly symbolic and you should not take the individual images too literally. They're open to a wide variety of interpretations.
That said, the passage doesn't say anything specific about bringing peace, so the main point seems to be that the speaker feels enough at ease to enjoy himself and have a good time. Also, he doesn't even have to do any of the cooking!
"Anointment" is a sacred act of setting a person apart and and making him holy. It is symbolized by rubbing oil on the person.
There's so much wine (or insert preferred delicious beverage here) in his cup that the liquid is literally overflowing the cup. God doesn't just provide enough, He provides more than enough.