The world of Toril is literally a magical place. Magic permeates the people as well as the land. Every town is home to mighty temples venerating the deities and housing clerics who call upon divine power to heal injury, ward against evil, and defend the lives and property of the faithful. Subtle and astute wizards stand by (and sometimes behind) the throne of every land, turning their formidable powers to the service of their lords. Aberrations made by ancient magic seethe and hunger in the dark spaces beneath the world's surface, awaiting the chance to feed. Even the most unimaginative fighter or most brazen rogue quickly learns to respect the power of magic, or sees her career as an adventurer come to a spectacular and ghastly end.
Mortals cannot directly shape raw magic. Instead, most who wield magic make use of the Weave. The Weave is the manifestation of raw magic, a kind of interface between the will of a spellcaster and the stuff of raw magic. Without the Weave, raw magic is locked away and inaccessible - an archmage can't light a candle in a dead magic zone. But, surrounded by the Weave, a spellcaster can shape lightning to blast her foes, transport herself hundreds of miles in the blink of an eye, even reverse death itself. All spells, magic items, spell-like abilities, and even supernatural abilities such as a ghost's ability to walk through walls, depend on the Weave and call upon it in different ways.
The exact nature of the Weave is elusive because it is many things simultaneously. The Weave is the body of Mystra, the goddess of magic. Mystra has dominion over magic worked throughout Toril, but she cannot shut off the flow of magic altogether without ceasing to exist herself. The Weave is the conduit spellcasters use to channel magical energy for their spells, both arcane and divine. Finally, the Weave is the fabric of esoteric rules and formulas that comprises the Art (arcane spellcasting) and the Power (divine spellcasting} Everything from the texts of arcane spellbooks to the individual components of spells is part of the Weave. Magic not only flows from source to spellcaster through the Weave, the Weave gives spellcasters the tools they need to shape magic to their purposes.