Since it is a phrase that is pushing 400 years old, it deserves a some in-depth discussion, methinks, as do many of the bards more esoteric phrases deserve.
The most explainable part of this sentence is the use of the word "coil". Most of us (21st century people) take the meaning of 'coil' as "A series of connected spirals or concentric rings formed by gathering or winding" (as lifted from the The American Heritage Dictionary).
However, in Shakespeares' time, 'coil' also had a somewhat different, although related, meaning. The meaning I am talking of, courtesy of our very own Webster, is "To encircle and hold with, or as with, coils". So with this definition taken into effect we realize that good William did not mean "a mortal loop of wire", but instead the inferred meaning of mortality wrapped around something.
The next article is the 'shuffle off' part. Shuffle, in this sense, means to do something slowly or unceremoniously (e.g. shuffling walk), and so "shuffle off" would be in the same realm of meaning as 'discard'.
So, putting all this together, we can give a fairly good (if longwinded) translation from Williams' middle-English to our modern tongue:
"to shuffle off this mortal coil"
Means
"To remove the mortality that is bound around me, holding me to the world of the living."