When would you use a semicolon in a sentence

A semicolon is used to join two or more ideas in a sentence, those ideas are then given equal position or rank. Some people write with a word processor; others write with a pen or pencil. Use a semicolon between two independent clauses that are connected by conjunctive adverbs or transitional phrases.

You would use a semicolon to joing or form a bond between two or more sentence without using a fullstop..When you use a fullstop in a sentence there is a pause but when you use a semicolon there is not for example it would be read like this..
I saw my father today.*pause because of the fullstop*He was wearing a blue shirt. 
I saw my father today;he was wearing a blue shirt.