You can join independent clauses in several ways: with a comma and a coordinating conjunction, with a colon, with a dash, or with a semicolon. Semicolons provide writers with subtle ways of signaling closely related clauses. The clause following a semicolon often restates an idea expressed in the first clause; it can also expand on or present a contrast to the first.

Immigration acts were passed; newcomers had to prove, besides moral correctness and financial solvency, their ability to read.

—MARY GORDON, “More Than Just a Shrine”

In this example, Gordon uses a semicolon to lead to a clause that expands on the first one. The semicolon also gives the sentence an abrupt rhythm that suits the topic: laws that imposed strict requirements.

A semicolon should link independent clauses joined by conjunctive adverbs such as therefore, however, and indeed or transitional expressions such as in a way, in fact, in addition, and for example

The circus comes as close to being the world in microcosm as anything I know; in a way, it puts all the rest of show business in the shade.

—E. B. WHITE, “The Ring of Time”

If two independent clauses joined by a coordinating conjunction contain commas, you may use a semicolon instead of a comma before the conjunction to make the sentence easier to read.

Every year, whether the Republican or the Democratic Party is in office, more and more power drains away from the individual to feed vast reservoirs in far-off places; and we have less and less say about the shape of events which shape our future.

—WILLIAM F. BUCKLEY JR., “Why Don’t We Complain?”