Resonance (レゾナンス Rezonansu?) is the process that is used to determine a person's compatibility with a Dragon. The ISDA's conceived process involves an artificially-made Dragon egg extracting DNA from its expected human counterpart. How an original Dragon from Thanatos succeeds in obtaining a Resonance with a human is unknown, but it appears as though they can achieve it without the human's consent, and the human may not even be aware that they have completed a Resonance with a Dragon.
It is said that without a successful Resonance with a Dragon, one will not be capable of controlling a Dragon. Also, as mentioned by Akira and Machina, when a Dragon makes a Resonance with a human, it is only then that a Dragon can truly understand what having a soul means.