Abeir-Toril, or commonly just Toril for short, is one of many planes in the Forgotten Realms campaign setting, and is considered to be the equivalent of Earth. Abeir-Toril means "cradle of life" in archaic, and it's often also referred to as the Prime Material Plane.
Abeir-Toril is home to many continents. Four of them, which are listed below, are the most common, described in the Forgotten Realms Campaign Setting book. Other continents include Osse, Anchorome, and Katashaka, though there are those that are yet to be discovered. Underdark, while not truly a continent, supposedly spans all of Toril, and is located deep underground.
Faerûn is roughly in the center of Toril, and could be perceived as Abeir-Toril's equivalent of Europe. Out of all the continents, Faerûn is the most versatile, and more often than not, countless adventures take place within this continent. The majority of Persistent Worlds are set in Faerûn, as well as all of Neverwinter Nights games so far.
East of Faerûn lies Kara-Tur, a continent twice as large, and whereas Faerûn is Toril's equivalent of Europe, Kara-Tur is the equivalent of the Far East. It's famed for silk, spice and gold. Its gorgeous landscapes and awe-inspiring buildings are also worthy of note.
West of Faerûn, across the Trackless Sea, lies Maztica, a continent that is yet to be properly explored. It's been discovered by mercenaries from Amn a decade ago, and has since then attracted merchants and explorers alike. This land is not uninhabited, however, and the natives are far from friendly.
Zakhara is said to be the best known and most frequently visited of Faerûn's neighbouring continents. It is located to the southeast of Faerûn, just beyond the Great Sea. It is described as a land of great deserts, lush oases, and powerful genies. Rumour has it that it is home to demon-haunted cities and faithless sorcerers who wield strange magic.