Semicolons have two distinct functions in English sentences. First of all, they allow you to connect two independent clauses in a single sentence. Often a writer chooses to do this to achieve a more flowing effect; the semicolon tells the reader that he has encountered a full stop, but implies that there is a close connection between the two independent clauses （I for one do this a lot; it often just sounds right）. Using a period to separate two independent clauses has a more conclusive effect. It forces more of a pause on the reader's part.
Second, semicolons replace commas when you write lists or series with internal commas （that is, where commas occur within one or more items）. In such cases, separating the items with other commas is confusing:
Hobbes's Leviathan has many memorable passages: his audacious view of human beings as mere mechanical constructions, his evocation of a brutish, savage state of nature, his establishment of a binding, permanent social contract to protect individuals, and his refusal to place any limits on the power of a duly established ruler.
To fix, make sure the main items are separated by semicolons （note where the commas are retained—within each main item）:
Hobbes's Leviathan has many memorable passages: his audacious view of human beings as mere mechanical constructions; his evocation of a brutish, savage state of nature; his establishment of a binding, permanent social contract to protect individuals; and his refusal to place any limits on the power of a duly established ruler.
Some people think that because semicolons look like fancy commas, and sometimes work like commas in lists, they can be used anytime a writer needs a comma but wants a fancy or formal effect. This is a mistake. Commas and semicolons have different grammatical functions. People also sometimes think semicolons are fancy colons. They are not. See the next item.
Second, semicolons replace commas when you write lists or series with internal commas （that is, where commas occur within one or more items）. In such cases, separating the items with other commas is confusing:
Hobbes's Leviathan has many memorable passages: his audacious view of human beings as mere mechanical constructions, his evocation of a brutish, savage state of nature, his establishment of a binding, permanent social contract to protect individuals, and his refusal to place any limits on the power of a duly established ruler.
To fix, make sure the main items are separated by semicolons （note where the commas are retained—within each main item）:
Hobbes's Leviathan has many memorable passages: his audacious view of human beings as mere mechanical constructions; his evocation of a brutish, savage state of nature; his establishment of a binding, permanent social contract to protect individuals; and his refusal to place any limits on the power of a duly established ruler.
Some people think that because semicolons look like fancy commas, and sometimes work like commas in lists, they can be used anytime a writer needs a comma but wants a fancy or formal effect. This is a mistake. Commas and semicolons have different grammatical functions. People also sometimes think semicolons are fancy colons. They are not. See the next item.