Basically it's because it buffers you very, very well against creature loss. If you're playing a weenie deck it protects you from deck-clearing spells. Or if you're sacrificing creatures, this card gives you extremely cheap, essentially unlimited new draws. The equip ability means you can just reuse it over and over again.
It's also very wide-ranging - almost any competitive deck is going to be better off having a few of these around, so it distorts the format. The basis for that statement is discussed in this very detailed article from the development team:
Skullclamp was banned in Standard, frankly, because it was everywhere.
Every competitive deck either had four in the main deck, had four in
the sideboard, or was built to try and defend against it. And there
were a lot more successful decks in the first two categories than in
the third. Such representation is completely unhealthy for the format.
Your deck has to either have Skullclamps, or have Skullclamp in its
crosshairs—a definitive case of a card “warping the metagame.”
Look, for example, at the Top 8 decks from Ohio Valley Regionals. Or
at those from the more recent German Nationals. Combined, those 16
decks contained 58 out of a possible 64 Skullclamps. Never in my
memory have I ever seen a card show up in those numbers.
It's interesting to note that the development team themselves completely underestimated the power of this card. The story of how it made it to release, discussed in the linked article, is quite fascinating.