Immortality, in general, is the state of living indefinitely. While precise details can vary, this may involve an inability to be killed and an indefinite life expectancy with regard to natural causes. The impact of this on mental health is sometimes speculated about.
In EGS, "Immortals" (previously known as fairies) are entirely immortal and generally maintain sanity by voluntarily resetting periodically. They can also be forced to reset. This results in a complete regeneration, reminiscent to the immortal phoenixes of mythology, which does not inherently retain prior memories, although this can be worked around in the case of voluntary resets given due preparation. They have generally been equated with the "Ancients" of the griffins' side of the universe.
Aberrations prolong their lives by feeding on humans. It is possible (but not confirmed yet) they can extend their lives indefinitely. They can regenerate even very serious wounds, however they can be killed by magic or magic weapons.