Semicolons are often used when a second independent clause restates the content of the first independent clause. Here is an example:
The blizzard has grounded all flights at the airport; planes are sitting on the runway, waiting for permission to take off once the storm ceases.
Here, the second sentence more or less restates the first sentence, so a semicolon is appropriate.
Semicolons are also frequently used to help emphasize cause-and-effect relationships. Here is an example:
The FLCA received stockholder approval for conversion of all protected stock to at-risk stock; this action will significantly strengthen the FLCA’s capital position.
Here, the first independent clause describes an event that happened, and the second independent clause describes what will happen as a result of the event. The semicolon helps emphasize this relationship.
The choice between a period and a semicolon in such instances is one of style as well as logic.
Sometimes when two short clauses are logically connected, it’s appropriate to combine them with a semicolon to avoid having short, choppy sentences. Here is an example where the connection is pugilism and numbers:
The record for consecutive victories in professional boxing belongs to Rocky Marciano with 49; Roberto Duran is second with 41.
Here is an example from Winston Churchill that uses a semicolon to emphasize contrasting ideas in two clauses:
A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty.