What does it mean when something has "no self-nature"?

I was reading on some later Buddhist and Mahayana sutras and kept seeing the principles along the lines of "all phenomenon have no nature of their own and are thus empty." I've studied on scriptures like this before, like the Heart Sutra, but I don't think the Pali Canon or Tripitaka mentions anything about this doctrine. I'm curious what exactly later Buddhists meant by this, and if the Buddha actually taught this doctrine or if Sunyata has basis in the original sutras. Thank you to all.