ImprintAn ability word has no rules meaning of its own. It groups abilities with similar themes; the text following it explains this card’s effect. (CR 207.2c) — Whenever a player casts an instant or sorcery spell from their hand,
exileTo exile an object, move it to the exile zone from wherever it is. See rule 406, “Exile.” (CR 701.13) it instead of putting it into a graveyard as it resolves.
At the beginning of your upkeep, if there are four or more cards exiled with this artifact, choose one of them at random. You may
castTo cast a spell is to take it from the zone it’s in (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. A player may cast a spell if they have priority. See rule 601, “Casting Spells.”
To cast a card is to cast it as a spell. (CR 701.5) it without paying its mana cost.