"Tizita" is a traditional Ethiopian tune that crops up over and over again in Cutting for Stone, holding the storyline together. It first shows up when Ghosh is visiting a prostitute:
"On the radio the muffled twang of a krar repeated a six-note riff from a pentatonic scale that seemed common to all Ethiopian music, fast or slow. Ghosh recognized the song, a very popular one. It was called 'Tizita'; there was no single equivalent English word. Tizita meant 'memory tinged with regret.' Was there any other kind, Ghosh wondered." (2.11.85)
The title of the song—"memory tinged with regret"—reflects that fact that memory is one of the book's major themes. For Ghosh, memory will always carry regret; perhaps the fact that the past is unchangeable makes it always a little bit sad. The song is mentioned at various points in the novel to reflect the impossibility of going back and making wrongs right.
Later, there's an entire chapter called "Tizita," in which Marion describes his very first memories, those he had as a baby. Almaz, his nanny, sings the song to him as she gives him her breast to play with as a pacifier. This early connection to the maternal and to birth is what Marion brings with him to America later on, when he meets Ethiopians in exile.
The Ethiopians in exile share their memories of their homeland by sharing their recordings of the song: "They are eager to share, to thrust that song in my hands, as if only 'Tizita' explains the strange inertia that overcomes them" (3.17.25). The song represents Ethiopia for the exiled people, so it's clear that these people's memories of Ethiopia are "tinged with regret." They can't go back, and they can't change what's done—but they can remember.