The Snowball strategy of debt reduction is used when paying off more than one liability simultaneously. Extra payments are made on one liability first, while paying steadily above the minimums on the remaining debts.  This works for households with variable cash flow income as well as fixed income streams. Liabilities can be investment accounts as well as loans, anything that sucks up cash.   
The main payment, increases in size as it rolls over each successive liability, essentially snowballing debt payments. The borrower focuses on paying off one debt faster than the others, so that there is a greater momentum to pay off the remaining debts. No payments can be missed on any accounts. In theory, by the time the last debts are reached, the extra cash flow previously paid toward the earlier liability’s, will grow quicker, like snowballs rolling downhill gathering more snow and momentum.
Payments can be made in an amount greater than the minimum amount on all of the debts, but the majority of the debt repayments are funneled to pay off one liability at a time as quickly as possible. As each debt is killed off, cash flow is moved on to the next, with the same aggressive accelerated repayment plan used on the first.
The effect on each liability is increased by the cash flow diverted from the previously mortified debts. One benefit of snowballing the smallest-balance first is the psychological feeling of getting to freedom.  A benefit of snowballing the highest rate of interest first, is reduced interest costs, and a quicker amortization of the principle.  The benefit of first “snowballing,” the liability that bears most on your mind, priceless.
Snowball 1400s, from snow + ball the image of a snowball increasing in size as it rolls along had been used since at least 1613, to throw snowballs at 1850, to make snowballs 1680s, Snowball's chance (in hell) is recorded by 1910.  to increase rapidly 1929