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) — When this artifact enters, you may
exileTo exile an object, move it to the exile zone from wherever it is. See rule 406, “Exile.” (CR 701.13) two target sorcery cards from a single graveyard.
Whenever a player casts a card, if it has the same name as one of the cards exiled with this artifact, you may copy the other. If you do, 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) the copy without paying its mana cost.