In short: the debt avalanche and the debt snowball are two ways to repay several debts: with the avalanche you clear the most expensive one (highest rate) first, with the snowball the smallest one first.
Simply put: in both methods you pay the minimum on all debts and put everything extra towards one. The avalanche is mathematically the cheapest. The snowball gives quick small wins that keep you going. A study by Gal and McShane (2012) links closing individual debts with a higher chance of repaying everything.
Example: a credit card of €1,000 at 24 %, a consumer loan of €3,000 at 10 % and an instalment plan of €400 at 15 %. Avalanche: the card first. Snowball: the €400 first.
Watch out: the method you will stick to is the better one for you. Secured debts and basic needs keep their priority in both methods.
Source: Pecuvo Module 8, Principle 3; Gal & McShane, Journal of Marketing Research 49(4), 2012 — https://doi.org/10.1509/jmr.11.0272