Which nouns get the definite article? This question can be tricky enough when English is not one’s native language, but there are also differences in usage among US, UK, and other variants of English. “She’s in the hospital” in the US becomes “She’s in hospital” in England. Various US government officials have recently started dropping the article before the word “wall,” making them sound caveman-like (“We must have Wall!”), while in other corners of Washington, D.C., it seems like those who are most likely to say “She’s in CIA” are those who are in fact also in the CIA (as most civilians refer to the agency).

And all of this is before one considers languages with gendered nouns and the masculine, feminine, and neuter articles that accompany them.

But in English, anyway, countable singular nouns usually require an article.

The ant fell off the log.
The definite article, as opposed to its twin siblings “a” and “an,” the only two other articles in English, can denote something commonly understood to be known to both writer and reader. Compare to:

An ant fell off a log.
I think of this as the “once upon a time” construction when editing fiction, as in, “Once upon a time, there was an ant that fell off a log.” The ant and the log are being introduced to the reader; they are not yet of a shared understanding.

Plural nouns, proper nouns and uncountable nouns usually don’t require an article.
Ants fell off a log. (plural noun, indefinite noun)
Humpty-Dumpty fell off a wall. (proper noun, indefinite noun)
Society descended into Hell. (uncountable noun, proper noun).

Uncountables can be tricky—cf. the future, the universe, but time, space:

The formicid timeship Vespoid, the last ship of her kind in the universe, hurtled into the future.

Vespoid, the last formicid chronofreighter in space, hurtled through time.

Sometimes the definite article is used to help represent a group or class in a given situation.

The age of humankind is done—the Age of the Ant has begun.

“The Ant” as a noun phrase here makes it more clear that ants are being referred to as a comparative class of living things than simply “ants” would. “The Ant” is drawing a parallel to, and making a distinction from, another class: the human. We have a separate word for humans as a class, though—”humankind,” an uncountable noun needing no article. (“The Age,” as with many other nouns representing spans of time, also gets the definite article.
Cf. the Ice Age, the Renaissance, the eighteenth century, the seventies.)

There is so much more to the use of the definite article and other determiners still to be discussed. But for the basics, as usual, GrammarGirl has you covered. And Education First lists some good examples of when the definite article should be used.