Single and double quotation marks are two different forms of a common typographic mark, and knowing when to use them can be a bit tricky at first. Matters of style are always up for a great deal of debate, and the choice of single or double quotation marks is largely stylistic, but with a bit of knowledge you can understand why some people choose to use one over the other.
First, let’s define what exactly these marks are. Double quotation marks are what most Americans think of as simply quotation marks, two lines that may be straight or curved, enclosing text "like this." Single quotation marks, on the other hand, are the one-lined version of these, either a single straight line, or a single curved line, which the British usually refer to as an inverted comma, 'like this.' Strictly speaking, both single and double quotation marks should be of the curved variety, but it is more and more common to see apostrophes and straight-quotation marks, the straight-lined counterparts, used as quotation marks as well.
In American English, the most basic rule of single and double quotation marks is simply that double quotation marks should be used by default for enclosing quotations. Single quotation marks, on the other hand, are used for enclosing quotations that exist within quotations. In British English, however, this standard rule is inverted, with the default mode being the inverted comma, and double quotation marks being used only for quotes within quotes. Over time, however, this has gradually shifted, and it is now not uncommon to see many followers of British English begin with double quotation marks.
The different types of quotation marks may also be used as a way to offset a single word or phrase within a sentence, when nothing is actually being quoted. This is usually meant to denote that the writer is intending the word in an ironic or sarcastic matter. It may be used for other reasons as well, however, such as in the sentence: On the map, 'X' marked the spot.
Here again, we have a cultural difference on when to use single and double quotation marks. The American standard is still largely to use double quotation marks for offsetting a word, sometimes referred to as a "scare quote," while the British standard is to use inverted commas. This distinction is largely retained, and it is relatively rare to see a writer of British English use double quotation marks to offset a single word or phrase.
This is all even further complicated by the fact that Americans often use the British standard of the single quotation mark when offsetting a word. And, when single or double marks are used for this purpose, it is common to also adopt the British standard of placing punctuation outside the quotation mark, as in ending a sentence with 'like this'. Normally in American English punctuation is placed within quotation marks.