A comma is one musical beat, a semicolon is two, a colon is three, and a full stop is four.

A comma is one musical beat, a semicolon is two, a colon is three, and a full stop is four.

I borrow this comparison from Lynn Truss’s brilliant Eats, Shoots and Leaves. Sometimes a main sentence needs a brief buffer between itself and a dependent clause, and that’s what the comma is for. When it needs a buffer between the main sentence and an independent clause, that is the function of a colon. And when you need a nuanced pause somewhere in between, that’s when we draft the semicolon.
It’s helpful to think of the semicolon as a really strong comma, and the colon as almost a period. Also, when a sentence segues into something akin to a list, the colon demarcates the sentence from the list and the semicolon separates the elements on the list from one another.
I sometimes use the em-dash (double hyphen) and semicolon interchangeably, but if I need two pauses of that magnitude in one sentence, I use the em-dash.