The Afterlife proper is called in the traditional sources olam habah, or the World to Come. However, the same term, "olam habah," is also sometimes used to refer to the renewed utopic world of the future -- the World of Resurrection, olam hat'chiah.¹

 

The former is the place righteous souls go to after death -- and they have been going there since the first death. That place is also sometimes called the World of Souls.² It's a place where souls exist in a disembodied state, enjoying the pleasures of closeness to God. Thus, genuine near death experiences are presumably glimpses into the World of Souls, the place most people think of when the term Afterlife is mentioned.

 

NOTES

1. Tosafos, Rosh HaShannah 16b, s.v. leyom din; Emunos V'deyos 6:4 (end), Raavad, Hilchos Teshuva 8:8; Kesef Mishnah, Teshuva 8:2; Derech Hashem 1:3:11.
2. Ramban (Nachmanides), Shaar HaGemul. According to the Ramban and other authorities, the "World of Souls" is also often referred to as Gan Eden, the "Garden of Eden."