Immortality is a trait that is possessed by vampires and possibly witches. Those who are "immortal" are able to live for several centuries, but do not appear to be centuries-years-old, but rather the age they were turned in the case of vampires, or age at a slower rate in the case of witches, or at least in Mrs. Flowers' case.
Immortal means literally not able to die from natural death, thus, not being mortal. Vampires are able to sustain injuries that would instantly kill a mere mortal like being stabbed through the heart or being suffocated. As for witches, they may be able to die from a more vast range of injuries, but have a slower aging rate--appearing to be no more thatn 60, but be over 100 years old. Mrs. Flowers, a witch, appears as a 60-something-year-old woman, but has hinted that she's over 100.