The Seleucid Empire was one of the empires that was created after Alexander the Great died. The areas that he conquered were split up into four empires, one of which was the Seleucid Empire.
The Seleucid Empire was named after Seleucus, who was one of Alexander's generals. The empire that he controlled was an Asian one. It stretched from Turkey in the east to (for a while, at least) India in the west. The Seleucids were thrown out of India by the Mauryans rather quickly so India is not usually seen as part of this empire. Along the shore of the Mediterranean, the empire reached as far south as Lebanon.
The Seleucid Empire lasted to some degree until the first century BCE. By that point, it had been much reduced in size and was centered in what is now Syria.