What does "order of magnitude" mean. What does it mean if something is an order of magnitude larger?

A number written in scientific notation has the form [A * 10^{b}],

where A (the mantissa) is in the range (-10,10) and b (the ordinate) is a real number.

The order of magnitude of that number is the value of the ordinate (b).

So when something is an order of magnitude larger that that, its ordinate value is 1 greater than the ordinate of the reference.

However, the notion of order of magnitude is not limited to numbers where 10 is the base for the ordinate. When a number is written in the form [A * B^{b}], where A is in the range [-1,1], B is a positive real number and b is a real number, the notion of order of magnitude remains the same: b is the order of magnitude, and one order of magnitude larger would be b+1.

In practice, this frequently occurs where the logarithm of an amplitude is used to characterize a variation -- like the loudness of something (measured in dB) or like the strength of an earthquake as measured on the Richter scale; in both cases, a difference of 1 between measures implies an exponentially related difference in amplitude of variation.