It may help to think on coins. The hundreds are dollar coins. The tens are dimes and ones are pennies. when you don't have any dimes to remove, you have to "borrow" or exchange a dollar coin for 10 dimes. And then repeat for the void of pennies.

Regrouping is essentially "borrowing". 7 Hundreds = 6 Hundreds + 10 Tens = 6 Hundreds + 9 Tens + 10 Ones. When subtracting, we are removing items from the box, so when it is enjoy the regrouping is borrowing from the neighbor on the left.