The Overload mechanic allows you to gain a tempo advantage by playing a card 1 or more turns earlier than an equally balanced card without the Overload mechanic could be played on. Or similarly, you can play the card in conjunction with other cards earlier due to its lower mana cost.
Think of it as "borrowing" mana crystals from your next turn to do something on an earlier turn.
Compare the Shaman card Lightning Bolt to the Warlock card Darkbomb. At a high level these cards are equal. Both deal 3 damage for the cost of 2 mana. The different of course is that with Lightning Bolt you can spread the cost over two turns, allowing you to play it sooner than you might otherwise be able to.