A colon is a pause like a semicolon, but it is used to introduce something that follows. For example:
This study is important for a number of reasons:
The hypothesis can be stated as follows:
The conferences will be held in the following cities: Vancouver, Edinburgh, Sydney, Dublin and Cape Town.
The colon can also be used to introduce a quotation, for example:
Shakespeare expresses this dilemma in Hamlet:
Whether ’tis nobler in the mind to suffer
The slings and arrows of outrageous fortune,
Or to take arms against a sea of troubles,
And by opposing end them?
Capital or small letter after a colon?
Generally, a colon should be followed by a small letter:
This approach has a number of advantages: firstly, …
Unless a name or other proper noun:
Several American writers spring to mind: Herman Melville, Walt Whitman, Tennessee Williams and Ernest Hemingway for example.
Or a subtitle:
A Whole New Ball Game: A Recent Discovery in Meso-America
In some reference styles, a colon is used to divide the year of publication from the page number, either with or without a space after the colon:
Rossi (2014: 438)