When you kill a monster (or sheep, or cows, etc. etc.), it will drop little green orbs. Pick those up, and you'll notice your XP bar, the bar above below your health/hunger, will fill up. Every time it fills up, you'll gain a level. Levels are required to enchant items. The better the enchantment, the higher the level required to enchant it. Once you enchant an item, those levels will be subtracted from your overall total.
Hope that clears some things up!
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