Let's look at each ability:
Equipped creature gets +1/-1.
Normally, you wouldn't want to equip this to a creature with toughness 1 because that would cause it to die (as a state-based action). However, the next ability makes it desirable to do so:
When equipped creature dies, draw two cards.
Equipping Skullclamp to a creature with toughness 1 gives you two cards at the cost of that creature...
Equip {1}
...and one mana. (Note that equip is sorcery speed.)
Considering that it's generally trivial to create 1/1 creature tokens, this is a small price to pay. Furthermore, equip is a repeatable action, so if you have some mana and a handful of these tokens on the battlefield, you could easily draw four, six, or even more cards. The result is an artifact whose combined effects are tantamount to this activated ability:
{1}, Sacrifice a creature with toughness 1: Draw two cards. Activate this ability only any time you could cast a sorcery.
In essence, in decks that use small creature tokens, Skullclamp nearly duplicates the effect of Ancestral Recall at only a marginally higher cost. To make matters worse, Skullclamp itself only costs one mana to cast and doesn't require any colored mana, making it usable in any deck.
This is a classic example of a design oversight resulting in a card that looks innocuous at first glance turning out to be seriously broken upon further inspection.