Parentheses are not the most common form of punctuation, but it helps to know how they are used. Here is a good explanation of how and when parentheses are used from the website, www.english.answers.com

“While commas are used to offset information that is closely related to the topic of the sentence, and dashes are used to indicate an abrupt shift in thought, parentheses are used to illustrate supplemental information that is not crucial to the original sentence. “
Google defines this punctuation form as
“parenthesis
noun
plural noun: parentheses
a word, clause, or sentence inserted as an explanation or afterthought into a passage that is grammatically complete without it, in writing usually marked off by curved brackets, dashes, or commas.
a pair of round brackets ( ) used to mark off a parenthetical word or phrase.”

Parentheses, or brackets, are used for extra information which is included in the sentence, but not necessary to it.  You use it when you want to include the information, but it needs to be de-emphasized.  Numbers, letters, dates, sources , as well as extra but unnecessary comments, that are not as important as the information in the rest of the sentence are placed in parentheses, which are always a pair.

examples of parentheses use

“I had one of those ancient teddy bears (the ones produced by Sieff in Germany) that I was able to give to the little girl.”
“My very photogenic mother died in a freak accident (picnic, lightning) when I was three…” Vladimir Nabokov Lolita

You must use square brackets not parentheses in a quote when you must add a word to make the sentence or phrase clearer.  Writingcommons.org explains the difference between square brackets and parentheses:

“When writers insert or alter words in a direct quotation, square brackets—[ ]—are placed around the change. The brackets, always used in pairs, enclose words intended to clarify meaning, provide a brief explanation, or to help integrate the quote into the writer’s sentence.  A common error writers make is to use parentheses in place of brackets.”
“Helen Keller turned to Socialism because “[she ] learned that the power to rise in the world is not within the reach of everyone” – James Loewen
The most specialized forms of punctuation are parentheses, brackets, and ellipsis points. Since they are used less frequently than any other punctuation mark, you can assume that proper application of each occurs under unique circumstances.