What do you call an inscription that appears on a tombstone or burial place?

The term used for an inscription that appears on a tombstone or burial place is "epitaph." An epitaph is typically a brief statement or phrase that commemorates the deceased, often summarizing their life or expressing sentiments of love and remembrance. This literary form serves both a commemorative purpose and an artistic expression, often encapsulating the essence of the individual's life or the sentiments of those left behind.

While "obituary" refers to a notice of a person's death, often including details about their life and funeral arrangements, it is not something inscribed on a tombstone. "In Memoriam" typically denotes a broader memorialization or tribute that may involve various forms of remembrance beyond the physical inscription found on a gravestone. "Inscription," a more general term, can refer to any writing engraved or printed on a surface but does not specifically point to the memorial aspect associated with epitaphs. Thus, "epitaph" is the precise term that conveys the meaning intended in the question.