What it does
I'm not aware of a Magic: The Gathering keyword or ability called "Devouring Monster." This doesn't correspond to any official keyword, ability word, or mechanic in the game.
You may be thinking of a few similar things: Devour is a real keyword (a creature with Devour enters the battlefield, and you can sacrifice creatures to put extra +1/+1 counters on it). There are also cards with "Monster" in their names or the Monstrosity mechanic (paying a cost to make a creature monstrous, adding counters and often triggering an effect).
If you can clarify which specific card or mechanic you mean—or paste the rules text—I'll gladly break down what it does, the common rules pitfalls, and how it plays in Commander.
Iconic cards with Devouring Monster
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