The Accusative case identifies the direct object, answering "Whom?" (Wen?) or "What?" (Was?). Example: Ich sehe den Mann (I see the man) makes den Mann the direct target.
Conversely, the Dative case indicates the indirect object, typically the recipient. It answers "To whom?" (Wem?). In Ich gebe dem Mann ein Buch (I give the man a book), dem Mann receives the book indirectly.
Simply put: Accusative = direct target; Dative = indirect party. Practice is key!