Percentages (%)
When we say "Percent" we are really saying "per 100"
One percent (1%) means 1 per 100.
1% of this line is shaded green: it is very small isn't it?
50% means 50 per 100 (50% of this box is green) 

25% means 25 per 100 (25% of this box is green) 

Examples:
100% means all. Example:


50% means half. Example:


5% means ^{5}/_{100ths}. Example:

Using Percent

Because "Percent" means "per 100" think: "this should be divided by 100" So 75% really means ^{75}/_{100} And 100% is ^{100}/_{100}, or exactly 1 (100% of any number is just the number, unchanged) And 200% is ^{200}/_{100}, or exactly 2 (200% of any number is twice the number) 
Use the slider on the left side and try some different numbers (What is 40% of 80? What is 10% of 200? What is 90% of 10?) 
A Percent can also be expressed as a Decimal or a Fraction

Read more about this at Decimals, Fractions and Percentages.
Some Worked Examples
Example: Calculate 25% of 80
25% =  25 
100 
And  25  × 80 = 20 
100 
So 25% of 80 is 20
Example: 15% of 200 apples were bad. How many apples were bad?
15% =  15 
100 
And  15  × 200 = 15 ×  200  = 15 × 2 = 30 apples 
100  100 
30 apples were bad
Example: if only 10 of the 200 apples were bad, what percent is that?
As a fraction, 10/200 = 0.05
As a percentage it is: (10/200) x 100 = 5%
5% of those apples were bad
Example: A Skateboard is reduced 25% in price in a sale.
The old price was $120.
Find the new price.
First, find 25% of $120:
25% =  25 
100 
And  25  × $120 = $30 
100 
25% of $120 is $30
So the reduction is $30
Take the reduction from the original price
$120  $30 = $90
The Price of the Skateboard in the sale is $90
The Word
Percent vs Percentage
My Dictionary says "Percentage" is the "result obtained by multiplying a quantity by a percent". So 10 percent of 50 apples is 5 apples: the 5 apples is the percentage.
But in practice people use both words the same way.