In more detail
You pay the minimum on every debt and put all extra money on the smallest balance, whatever its rate. When it is gone, its payment rolls onto the next-smallest balance, so the payment "snowballs" as debts disappear. It usually costs a little more interest than the debt avalanche; the two are identical when the smallest balance also has the highest rate. See How Debt Payoff Strategies Work.
Why it matters
Clearing a whole debt in the first few months gives visible progress and fewer bills to track, and many people stick with it better because of that. A plan you finish beats a cheaper plan you abandon, but it helps to know what the motivation costs.
Example
With the guide's three debts (Card A $5,000 at 22%, Card B $2,000 at 15%, Loan C $800 at 9%) and $375 a month in total, the snowball clears Loan C in month 4, Card B in month 12 and Card A in month 28, with $2,050.44 of interest. The avalanche finishes in 27 months with $1,629.85, so the snowball costs $420.59 more and one extra month.
Common confusion
The avalanche orders debts by interest rate; the snowball orders them by balance.