I have a couple of gamer profiles that aren't used anymore but I can't find out how to delete them.
go to your settings and find system -> storage then click on the drive you use to save (Most likely your hard drive) Then go to profiles, find the one you want to delete there, click on it and select delete
so in short: settings -> storage -> hard drive -> profiles -> 'profileThatNeedsDeleting'
NOTE: You'll have to decide between Delete Profile Only and Delete Profile and Items
Delete Profile Only = delete the profile but keep the saved games and achievements
Delete Profile and Items = delete the profile and all the games and achievements that go along with it