orders of magnitude
Imagine trying to draw a number line that fits both the width of a hair and the distance to a galaxy on the same page. It is impossible with ordinary spacing — one would be a dot, the other off the edge of the city. The trick astronomers use is to count not the numbers themselves but how many times bigger one thing is than another in factors of ten. Each factor of ten is one 'order of magnitude'.
An order of magnitude is a step of x10. Ten metres is one order of magnitude larger than one metre; a hundred metres is two; a kilometre (1000 m) is three. We write big numbers in scientific notation to make these steps visible: 1.5 x 10^8 km, where the exponent 8 is what really tells you the scale. To say two quantities differ by 'three orders of magnitude' means one is about a thousand times the other. This is the same idea as a logarithmic scale, where equal spaces on a graph stand for equal multiplications, not equal additions — exactly how earthquake (Richter) and loudness (decibel) scales work.
Astrophysics lives and breathes in orders of magnitude because the quantities it deals with span dozens of factors of ten — from the size of an atom to the size of the universe is more than 40 orders of magnitude. Working this way, an astronomer cares first about the exponent (is a star a thousand or a million times the Sun's brightness?) and worries about the leading digits later. An 'order-of-magnitude estimate' deliberately gets the right power of ten while ignoring fine detail — a powerful first sanity check that often decides whether an idea is even plausible.
The Sun's mass is about 2 x 10^30 kg and the Earth's about 6 x 10^24 kg. Rather than wrestle with the full numbers, an astronomer notes the exponents differ by 6 — the Sun is roughly a million times heavier — and that single fact already explains why the Earth orbits the Sun and not the other way around.
The exponent carries the scale; comparing exponents is comparing orders of magnitude.
Because the scale is logarithmic, the gap from 10 to 100 looks the same as from 1000 to 10000, even though the second gap is a far larger number. This compression is the point — but it can mislead anyone reading a log graph as if it were linear.