In the words of Euclid:
Care needs to be taken with this definition. It is possible to create non-plane surfaces which can be generated solely by straight lines. Twist a deck of cards and the edges of the deck will no longer be plane surfaces, although the edges of the individual cards are as straight as before. The point to this definition is that any straight line lying partly in a plane surface lies wholly in that surface (unless intersecting it in just one place).
Also known as
A plane surface is usually referred to just as a plane.