The ten china figurines on the dinner table allude to the "Ten Little Indians" nursery rhyme, which is framed on the wall of each bedroom. They also represent the guests on Indian Island who are being bumped off by a crazed killer one by one. Each time a guest is murdered, one of the china figurines mysteriously vanishes.
This is a useful plot device, as it helps to build suspense. The disappearance of the figurines scares the living daylights out of the guests, as it really brings home to them just how much danger they're in. The china figurines are almost like toys to the murderer, a crucial part of the sordid little game they are playing with their guests. And the murderer's removal of each figurine perfectly symbolizes the callous, manipulative manner in which the murderer treats their victims.
The centerpiece on the table at dinner consists of ten china figures of indians. As each of the guests meets their fate, a china figure mysteriously disappears from the centerpiece. After the death of the first guest, Tony Marston, Vera makes the connection between the china figures, the verse from "The Ten Little Indians" poem, and the manner in which Marston died. After the second death, Mrs. Rogers, it is discovered that there are only eight china figures remaining in the centerpiece. This pattern continues as one by one, the guests meet their untimely end.