Most likely where the above band took its name, a skeleton key is a special key that forms a large set of keys that as a group can typically open any ward lock. Ward locks are the type with the 'classic' key-hole shape through which you can usually see through to the other side. Keys to this type of lock have a cylindrical shaft with a shaped square of metal on the end.
Contrary to popular belief, a single skeleton key will not open every ward-lock you come across, you need a whole set to get through MOST locks. You can never in theory open every ward-lock even with a thousand skeleton keys in your set as you can never cater to defeat all configurations of wards. The idea is that a set of skeleton keys will get you through as many locks as possible. The more keys in your set, the higher your chances of getting through a lock is.
To understand how a skeleton key works, you must understand how ward locks work. The key you use has a shaped square type piece of metal at the end. When the key is turned in the keyhole, the small holes and notches that gives the key-head its strange shape move past the 'wards', small metal barriers that stop the wrong key from turning inside. When the correct key is turned, once it has navigated the wards it hits the trigger mechanism to release the lock.
The principal behind the skeleton key is that you take the square piece of metal and reduce its shape so the tip of the key-head (part that hits the trigger) remains but most of the other keyhead metal (that in other keys are used to stop them opening locks they are not intended for) is removed.
The idea of this is that one key cut in a wierd manner like this would be able to overcome the wards in many more locks that it was originally intended for. Less metal on the keyhead, less chance it will hit a ward.
The reason you need a set of skeleton keys is because one shape of keyhead can and will get stuck on some wards in some locks, and your other keys in your set will succeed in passing them. To support the piece of metal that hits the mechanism (the key-head tip) the supporting piece on one skeleton key might hit something, whereas others will not. Another reason a set of skeleton keys are needed is because there are different sizes of key shafts/heads.
The skeleton key gets its name from being a normal key with as much of the spare stuff stripped from it as possible. Thus the key is a skeleton of its former self.
Skeleton keys do not work in tumbler locks as they operate on a different mechanism design. In order to open these locks you would require the tools and knowledge to perform lockpicking.