Every point in any given plane perpendicular to its direction of propagation has the same phase. Electromagnetic radiation in this form is necessary for x-ray diffraction. A wave emitted from a spherical source like a star or the sun can be treated as a plane wave if the source is sufficiently far away.
Analogy
If you were to hold a book above the floor so that the book is parallel to the floor, then drop it. Then do the same thing with another book, and another... The impacts would be like a plane wave hitting the floor. If the books were dropped at an angle, so that they hit the floor at an angle, your experiment would not be like a plane wave.
Schematic Representation of a Plane Wave
---------------------------------> direction of propagation
_-_ _-_ _-_ _-_ _-_
_- -_- -_- -_- -_- -_
_-_ _-_ _-_ _-_ _-_
_- -_- -_- -_- -_- -_
_-_ _-_ _-_ _-_ _-_
_- -_- -_- -_- -_- -_
Schematic Representation of a Non-Plane Wave
---------------------------------> direction of propagation
_-_ _-_ _-_ _-_ _-_
_- -_- -_- -_- -_- -_
_-_ _-_ _-_ _-_ _-_
_- -_- -_- -_- -_- -_
_-_ _-_ _-_ _-_ _-_
_- -_- -_- -_- -_- -_
Dropping Books on the Floor
In a plane wave fashion
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[_________] --- Book / Maxima
--- Empty Space / Minima
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[_Physics_]
________________Floor