Origins
Figure is one of English's great shape-shifters. It means a number, a body, a diagram, a statue, and a rhetorical device. All from one Latin word meaning 'something shaped'.
Latin figūra came from fingere ('to form, to mould'), and it meant any formed shape. A sculptor's figūra was a statue. A geometer's figūra was a triangle. A rhetorician's figūra was a patterned expression — what we still call a figure of speech.
English absorbed the word through Old French in the 13th century and kept every sense. The numerical meaning arose because written numbers are formed symbols — figures on a page. The bodily meaning came from the idea of a shaped form. The diagrammatic meaning preserves the geometric usage directly.
Word Formation
The compound words reveal the root's flexibility. Configure means 'to shape together'. Disfigure means 'to un-shape'. Transfigure means 'to reshape across' — to change form entirely, as in the biblical Transfiguration.
French took the word in a different direction. There, figure primarily means 'face' — the most visible shaped part of a person. English kept the broader meaning, allowing figure to serve as one of the most polysemous words in the language: six figures, a public figure, figure skating, figure of speech.