Magic's Lore is kinda long and to get the most out of it you'd have to read the books. Some are decent, most are eh and a few are quite bad.
In short, the players a "Planeswalkers" nigh-immortal beings who are capable of casting spells and hoping between dimensions. For the first half of magic's life it was about a planeswalker known as Urza as he tries to prevent the invasion of Phyrexia into other dimensions. It all eventually came to ahead and Phyrexia was destroyed along with Urza. The taint spread infecting some other planes. After that the lore spent time in various planes and exploring them like Innistrad, a plane ruled mostly by vampiric aristocrats, Ravinca a plane that is ruled over by 9 powerful guilds and Mirroden a plane made up of mostly non-organic life.