PLAIN is an adverb which means, simple and ordinary looking, with no decorations.

It is also used as an adverb to emphasize upon something

As a noun, Plain is also used to define a large flat area, with fewer trees

Sentences:

  1. She is wearing a plain dress.
  2. I mean, you took the wrong way home, that’s plain stupid.
  3. High mountains rise above the plain.

PLANE is a noun, commonly used to describe an airplane.

In mathematical terms, it is used to define a flat surface where a straight line joining two points can wholly lie.

Sentences:

  1. The plane is flying high, above the sky.
  2. Two planes intersect each other in a three-dimensional surface