I've set up iCloud music library but iMac still shows 25 G used, Why is this? I've set up iCloud music library on my iPhone, iPad and iMac. The music folder on my iMac shows about 25 gigs used. I thought the music was moved to iCloud.  What am I missing here and what should I do to free up that memory.

Over half of that 25 Gigs is 'Mobile Applications' which are apps on my iPad and iPhone. Can I delete these or move to my external drive?
It's not moved to iCloud; it's just uploaded, as a kind of backup. You can just remove the music via iTunes; it will ask you if you want to delete it from iCloud as well, or if you only want to delete the local copy.

Have you set up backup via iCloud for your iPhone and iPad? If so, you can delete the mobile applications; the apps themselves are not backed up (so they don't take iCloud storage space) but will be readily downloaded from the App Store archives when you restore a backup. (Backup via iCloud does take storage space, but for local files and settings.)

[EDIT]

Should you ever want to re-install an app to your iPhone and/or iPad that is no longer available on the App Store (or an older version of an app that's no longer available) then having a local copy is advantageous. 

However, assuming you have a backup regime in place (e.g. you have Time Machine enabled) then your iTunes library should already be backed up, so in theory you'd still have local copies of your apps available (at least until they're overwritten).