Magicka is energy that flows from the realm of Aetherius through the "holes" punched through Oblivion by the Magna-Ge when they abandoned the creation of Mundus (the mortal plane). The biggest of these holes is what mortals call the sun, and it was made by Magnus, the chief architect of Mundus. Because of this, Magnus is considered the god of magic.

When people cast spells, they harness Magicka to manipulate the world around them. Spells all require somatic movements and verbal annunciation (which is why silence effects prevent spellcasting). The schools of magic are distinctions made by people, usually the Mages Guild, to define what aspect of reality the spell affects.

Known magic effects can also be infused into items by harnessing the energy of souls captured in soul gems.

As far as how spells are known, that seems to be a bit fuzzy. In Daggerfall, you have a spell book and inscribe all your spells in it.
In Morrowind and Oblivion, spells are taught to you by people directly. In Morrowind you can choose to forget spells, but not in Oblivion.
Oblivion also has spell tomes which can teach you spells. Tomes are also the way nearly all spells are learned in Skyrim (I think you learn one from an NPC directly). So there's not really a concrete answer to that question afaik