What is a Colon?
A colon is used to expand on information. While semicolons are usually used to show a close connection between independent clauses, a colon simply tells you to check the succeeding series of elements to better understand the preceding sentence. 
Sometimes it's a little puzzling for writers when it comes to using a colon, but there's really not much to it. Simply consider it to be an arrow that directs you to more information, and you'll be fine. Thus, in sentences, colons are impressions that infer "which is/are," "as follows," or "thus." In the example below:
"There are two exceptionally brilliant students in my class: Peter and Paul."
The colon here informs that I'm about to tell you who the two exceptional students in my class are. The sentence might be read in a silent manner as;
"There are two exceptionally brilliant students in my class (and they are): Peter and Paul."
As exemplified above, colons can be used for enumeration by introducing a list of elements, but they can as well signal clarification to a preceding statement. Let's look at the following sentence. 
There are only two options when faced with a challenge; deal with it or give an excuse to run away.
The above statement silently reads as:
There are only two options when faced with a challenge (and they are as follows): deal with it or give an excuse to run away. 
In other cases, colons can be used to introduce a quotation, for example:
I love his favorite words: "keep trying or never get started."

Colons Separating Independent Clauses
Colons are also handy when separating two clauses that are independent, but only when; the succeeding clause has a direct relationship to the first or the second clause bears more of the emphasis. You can also decide to go with a period or semicolon for this purpose. However, colons sound slightly harder than the semicolon but softer than the period. Here are some examples;
He is obviously not an average runner: he always trumps his competitors.
The statistics are out: there are more women than men in the world.
There are different styles of introducing words after a colon. While British English doesn't permit capitalizing the next word with the exception of an acronym or proper noun, American English is more flexible. In any case, you'll want to use a capital letter to begin the next word if two or more complete sentences follow. For example;
My career goals are expressly clear: First, I will pursue a first class honors degree. Second, I will study abroad after graduation. Third, I will start my own firm.

Misuse of Colons
There are basic rules when using a colon. Avoid common pitfalls by not using a colon to separate a noun from its verb, verbs and their subject or object complement, objects from their prepositions, or subjects from their predicates.
So, it is wrong to say;
The two exceptionally brilliant students in my class are: Peter and Paul.
This is wrong since the verb "are" is separated by a colon from its subject complement (Peter and Paul). The correct statement is, therefore:
The two exceptionally brilliant students in my class are Peter and Paul.

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