In the same spirit: I laughed at this and upvoted it, but I don't know what the square cube law is or what it has to do with mechs. I don't really understand the joke and I'm honestly a fraud for upvoting it and engaging with it, at all.
Think about any part of your body... say your arm. Now imagine scaling it up to double the size.
Your muscles are now double the length but also have to move a doubled distance. That changes nothing.
That same muscle (it's roughly a tube) has doubled it's diameter, so it 2² = 4 times as strong because it's cross-section is a circle and the surface of a circle is (d/2)² * pi.
But your whole arm has doubled it's size in all 3 directions. So it's volume/mass is now 2³= 8 times as high.
So in short: double your size and you are 2² = 4 times as strong, but you also have to move 2³ = 8 times the mass. That's the square/cube thing that makes just scaling up impossible.
PS: Yes, if you ever wondered how you were so incredible good at climbing things when you were a child... small children are much stronger than you compared to their own body weight.
In addition to what others here have said, it is also the cause of scaling fall damage.
An ant falles down a mine shaft and doesn't even notice.
A mouse bounces and runs off.
A person breaks.
A horse splashes.
Surface area decreases max fall speed. Mass increases max speed. Mass times speed indicated how much force something feels at the end of the fall. The issue is, surface area scales as a square, Mass as a cube, and thus the bigger something has the less drag it has and the more energy it absorbs as it lands, getting hit coming and going.
The square-cube law is about how increasing the size of an object increases its volume much more rapidly. So if you make an ant, say, twice as large, it ends up 4 times as heavy (don't take these numbers as anything but an example, I'm pretty sure there's formulae and shit). For that reason, massive vehicles, like mechs, are impractical - something twice as large as a tank is gonna end up much more than twice-as-heavy.