Was just thinking about this one today and it is a little confusing!

Bartleby to the rescue:

A plain is “a broad, flat expanse of country,” and so the corresponding adjective means “level,” “lacking decoration,” “unpretentious,” and “uncluttered and obvious.” Used of persons, plain means “homely or lacking in beauty.” A plane is “a geometrically flat surface,” “a tool for smoothing wood to make it flat,” “a kind of tree,” and any of a number of specialized names for surfaces of like qualities, such as the planes of a glider or airplane. Plain and plane are homophones, but confusion can arise when you spell the name of the specialized flat surface you have in mind: is it a plane or a plain? Plain is topographical at the outset, and plane, geometrical, but from there on, your dictionary should be your guide.

bartleby