Eugene,
We had our first experience having a butler when we took advantage of an upgrade on our last cruise. He took the time to explain his position to me. He said to forget about any other service button on the phone except for butler. Your butler, or one of the other butlers depending upon the hours your butler works, come and take your order for room service and then deliver it to you. If something in the cabin is not working correctly, they contact the correct department and have it fixed. If you want a restaurant/spa reservation, or are hoping to have an extra reservation, the butler handles that for you. The butler unpacks/packs if you wish. The butler ensures that your laundry is picked up and returned to your suite. If you have bought too many packages to carry up to your suite, the butler will come and carry them up for you. The butler will bring you pre-dinner h'ordeuvres from the butler menu, located in your cabin, each day. If you plan a special event in your suite, the butler makes the arrangements and ensures everything goes smoothly.
We didn't use the unpacking/packing service, so I can't tell you first hand how it worked; nor did we use the carrying the shopping packages service. However, our butler did an excellent job helping plan and hold an anniversary party for friends in our suite.
I'll try and find my notes to see if I wrote down anything else.