What was Big Willy Shakes going for?
What is this coil he's talking about, anyhow? Well, in Shakespeare's day, coil meant to make a big fuss about something. So the line is literally saying that there is turmoil in this mortal life. It's just full of the hustle and bustle of everyday stuff (which Hamlet hates).
Hamlet may talk—and talk, and talk—about suicide, but what he's really concerned with is mortality, and the fact that our world is made of death and decay. (Yeah, we know that life looks pretty grim when you put it that way. Sorry.) From Hamlet's initial confrontation with a dead man's ghost to the final bloodbath, the play is trying to come to grips with just this problem: if we all die eventually, then does it really matter who kills us?
Yep, it just got real. But that's kind of the point of this speech. Hamlet is really seriously considering those big questions about life and death, and what it means to live. Chances are, Shakespeare is also hinting at the idea of the Fates controlling our lives. In Greek mythology, someone's life was measured in the span of a long thread on a coil. The Fates would cut the thread when someone would die. So Hamlet's suggesting this idea of the Fates cutting the cord whenever they wish, and the rest of us just waiting for the coil to unravel.
But Hamlet's also making a pun on coil here. He's using it to mean his body as well. The human body quite literally holds him—and his soul—back from immortality, because, it dies eventually. So Hamlet's saying that we all die, and our bodies and lives are full of tumultuous activity that doesn't really matter in the long run.