(Oriringally Posted Feb 11, 2016)
A semicolon is an excellent piece of punctuation and excellent people use it (sparingly).
Like any other piece of punctuation, the semicolon conveys information to the reader. Most readers do not consciously think about punctuation in this way, but this is the underlying purpose of all punctuation. A period is more than just a place to catch your breath and a new paragraph does more than make the page look less intimidating; these deliberate acts of punctuation relay to the reader clues about how ideas are connected.
The Oatmeal has a great explainer on the semicolon that is as funny as it is informative. Check it out! There are a number of other great grammar explainers on that site, but it can pass into vulgarity from time to time.
In the case of a comma, it tells the reader that the details on either side of the comma are intimately involved in the purpose of the sentence or phrase. A series of commas that separate words, phrases, or clauses generally show that the content between (and on either side) of the comma are equally important to the point being made. We don't say that connection when we read, but neither do we define each word on the page. This meaning is as part of the comma as it is a part of a word, and we internalize it even as we pronounce it. And we do pronounce our commas. They are a short pause, and by leaving space for them in our speech we must consider them as existing there as tangible as the words before and after them.
The long pause is a period, and it shows a degree of separation between one sentence/idea and another. This does not mean that the two are not related at all. Two independent sentences may be focused on the same topic and be logically separated by a period. They should be, in fact. The connection between the two sentences is not particularly special, however. We use a period when the two sentences/ideas do not show a connection that is more significant than those around it.
Semicolons provide that special relationship.
When a semicolon is used, the author is showing that the ideas being expressed are either especially connected to one another or that they are different in a way that merits paying special attention. This is a special connection between the ideas, and to use it correctly is not only to show that you are intimately familiar with the use of less common language structures, but to show that you so understand your topic that you recognize and can demonstrate that understanding through grammatical structure alone.
For Example:
The teacher had a professional way about him; his tie collection was astonishing.
The first thing to note is that grammatically, both sides of the semicolon can stand alone as sentences. These are called independent clauses, and combining them is the most common use of the semicolon. Because they could stand by themselves as sentences, it would be perfectly acceptable to separate them with a period. This would establish each sentence as a description that might help someone understand details of the teacher, in this case that he is professional and he has an impressive collection of ties.
The semicolon does not change the content of this description, but as a connector of ideas, it tells the reader that these two independent clauses are related not just to the overall idea of the teacher, but to each other. In this case, the suggestion is that his professionalism has a great deal to do with the variety of ties he wears. This actually reveals something about the speaker as well, because to her, ties = professional.
It should be noted that the comma DOES NOT work here. While it does show a connection between ideas, you cannot use a comma to connect two independent clauses. This is called a comma splice, and it is a common error. Don't do it.
More examples:
She wore the old sweater regularly; it belonged to her boyfriend. (This suggests that she wore it because it belonged to her boyfriend.)
I didn't order a drink from the bartender; he had a nasty cough. (It appears that the bartender may have been coughing into the drinks. Yuck)
She said you haven't lived until you have tried the white chocolate there; I think I can do without it. (The speaker seems to not want it because some specific person recommended it, possibly suggesting a grudge.)
Final Note: do not overuse semicolons. They show a special relationship and should not be used too frequently. If they are used too often, the value of them as a connector of especially related ideas is lost, in the same way that anything that becomes too common becomes less valuable. It is also worth mentioning that there are other uses for semicolons, primarily as SUPER COMMAS! I encourage you to look it up if you want to know more.
As an aside, when I was looking for an image to serve as the banner for this post, I noticed a TON of semicolon tattoos. I didn't use one, but I was curious to know why this was the case. It turns out that the semicolon has become a tattoo representing the ongoing fight against depression and suicide. Because the semicolon follows an independent clause, an author could choose to use a period and end the sentence there. By choosing not to do so, the author seems to express that there are bigger ideas worth exploring and experiencing.
As a metaphor for choosing not to commit suicide, the semicolon seems appropriate then. Choosing not to end that sentence - that life - and instead to connect it to something greater is a sign of hope. The creator of this movement has a site at Project Semicolon that is worth checking out, especially if you know someone suffering from depression. Theirs is a message of hope, and because they are using that semicolon exceptionally well, I must say that they are excellent people.