"I think, therefore I am."

I'm pretty sure most people in the English speaking world has heard of this famous quote of Descartes'. What exactly does it mean though? I'm not certain if my interpretation is correct, but to me it's saying: I am capable of thinking, therefore this proves that I exist.

If that's the case, wouldn't that mean that inanimate objects, for instance a rock, can't be proven to exist because they are not capable of thinking?

Just curious, are there any budding philosophers out there willing to enlighten me? =)

Well, I'm back from Penang... Had plenty of nasi kandar (like really A LOT), char kuew teow, laksa and various other hawker food and I've got an extra kilo in weight and a big irritating throat infection (the complete package: sore throat, runny nose, slight temperature etc.) to show for it. Aiks...