Lore: Magic -uesp.net
Magic is the general term used for the focusing of raw energy into various properties and for various purposes. This raw energy, often referred to as magicka, flows from Aetherius into Mundus by way of the sun and stars, and from it the Mundus was created. Magicka comprises every spirit, it is the energy of all living things and can be harnessed in a variety of ways. Despite thousands of years of study, there is an enormous amount of speculation about how magic is generated, how it might be used by Aedra and Daedra, and how it might flow between living things.
Spellcasting does not require vocalization.
Inexplicably tapping "arcane energies"1 by "force of will" is the only explanation I'd accept.
1. See my answer here, after the line break: If magic is real, can it be true that rational scientific thought should exclude it? -World Building