What is the relationship between my ideas and the things they purport to be representations of?

Descartes' answer:

You will remember that Descartes had put God forward as the guarantor of our senses' basic reliability. Our senses purported to tell us of a material world, and God would not have arranged for us to be systematically mislead. So we could be confident that there was a material world, and that our ideas gave us knowledge of it.