Xunker points to the Webster definition in his explanation, but he selects a verb form of coil, rather than the noun form ("shuffle off this mortal {noun}").
The noun form of the archaic definition of coil reads: "A noise, tumult, bustle, or confusion." Below this definition is indicated Shak., that is, the Shakespearean definition (the man wrote well enough that that English is referred to today as Shakespearean English, by us 21st-century types).
But even Webster's definition isn't quite fair. The Shakespearean meaning of the word was most certainly its "primary" definition, primary inasmuch as the bard intended it, but we cannot disclude the other noun forms of the word, which have very different meanings. Afterall, can Webster really be sure that the poet Shakespeare intended this or that particular meaning of the word? We cannot be certain, as we can never be certain in such cases; indeed, one value of a given word invariably influences the other, and the two are ultimately linked.
\Coil\,
n. 1. A ring, series of rings, or spiral, into which a rope, or other like thing, is wound.
The wild grapevines that twisted their coils from trec to tree. --W. Irving.
2. Fig.: Entanglement; toil; mesh; perplexity.
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