A geometric progression is a progression in which there is a constant ratio between terms. The value found by dividing any term by the term before it gives you the constant ratio.
Example 1
What is the next number in the progression 1, 2, 4, 8, 16, … ?
The ratio is = 
because 
. You could also have said that you're simply doubling each number to get the next number. So doubling the last number, 16, gives 32.
Example 2
What is the next number in the progression 3, 9, 27, 81, … ?
The ratio is 
because 
. You could also have said you are multiplying each number by 3 to get the next number. So multiply the last number, 81, by 3, which gives 243.