There are several methods you could use.
1. Rename, Move, and Copy files. Select the files in your playlist, then Library Tools > Rename, Move, and Copy.
CAUTION CAUTION CAUTION: This is a very powerful tool. It defaults to RENAME mode and will move your files unless you select COPY mode. Be careful
The dialog that appears has a lot of options. You'd want to set it to "copy" mode, and then check Directory, and specify the directory you want the files copied to. I would uncheck the other sections (filename, find & replace).
This method is simple, but it might not be what you want because it will just copy the files. It won't recreate the directory structure, so you file names might not have enough info for you to sort or search your files the way you want to. Presumably you want to do this so you can copy the files to an external media player, or play them on another computer via a thumb drive or something. Which brings us to #2.
2. Handheld Sync. MC includes a pretty nicely thought out system for syncing files with handheld players. This includes simply copying the files to a directory that you specify. Here's the wiki on it:
https://wiki.jriver.com/index.php/Sync_HandheldHandheld Sync let's you check off playlists and those playlists are synced to the directory you tell it. Later, if the playlist changes, you can sync again, and the changes are synced as well. Handheld sync also includes a file conversion option, so you can convert files to MP3, AAC, or other lossy formats during the sync process. This is optional, and useful for some people.
By default, Handheld Sync creates Artist and Album folders, so it's easy to identify which songs are which, based on the directory structure; which is logical. It also copies the actual playlists into playlist files (M3U or variants) so that handheld players can use these playlists to play the files.
Handheld sync takes a bit of setup time and some getting used to. But it's a really nice tool that might do exactly the job you are looking for.
Brian.