The description of the word you requested from the astronomical dictionary is given below.
An order of magnitude is a factor of about 10. Orders of magnitude are used a lot by astronomers and physicists, who study very small and very large things and so talk about numbers that may not be known very precisely but that have many zeros before or after the decimal point. If an astronomer says that some thing is three orders of magnitude larger than some other thing, then the astronomer means that the second thing is about 1000 times larger than the first thing. It could be 3000 times, or perhaps only 500 times, but not only 100 times or as much as 10,000 times.
For each extra order of magnitude, you must multiply by an extra factor of 10. Orders of magnitude are especially handy for very large numbers. It is easier to talk about 18 orders of magnitude than about the number one trillion (How many zeros did that have again in British English? And wasn't that different in American English?) or one million million million, or 1,000,000,000,000,000,000, or 10^{18}. 18 orders of magnitude is about the ratio between the diameter of the Earth and the diameter of an atom, and also about the ratio of the diameter of the visible Universe and the diameter of the Earth.