This is the Olympian ability to manipulate matter at the molecular level. It allows them to change the nature of the material by touch. This can be as simple as changing the color of an object to turning base metals into gold. It is believed that the ancient Earth science of alchemy was brought into existence by mortals trying to replicate this power.
When an Olympian touches a living creature they can manipulate the cells of that organism at the cellular level. They can mutate the DNA of an animal to create such monsters as the three headed dog Cerberus or the winged horse Pegasus. When transmutation is used on humans it can give them Olympian-like powers at the discretion of the god or goddess. It is how Demeter gives her daughters the ability to enhance the growth of plants or how Athena gifted Lady Ardella with the power of empathy.
What little is known about how transmutation works comes from Marcus of New Athens’ studies with the Goddesses Athena and Demeter (circa 999 AUC). He is the only scientist to ever be allowed to run tests on pre-transmuted and post-transmuted material to determine the nature of the change. He conducted over twenty experiments on living and non-living samples which were transmuted by the Goddesses.