When press R in Blender, I can rotate the plane about the axis from user view to origin.There is also a option to constraint the axis. When I ticked x axis, I expected that I will be able to rotate the plane about x axis shown by red in view. But it clearly doesn't work in this way, because by ticking or unticking whichever axis nothing special changed when rotated.
In general these:
Will start rotating whatever it is around the global x,y,z axises, and these:
Will start rotating around whatever transform type is listed in the box in the 3d View Header:
(Normal is equivalent to Local for objects, but averages selected normals when editing meshes.)
As an aside, if your objects are rotating around unexpected places check the left two buttons in this picture.
You might get the result you want if you change the Transformation Orientation to Local or View, then Press R, X, X. This will then let you rotate in Local or View mode, instead of Global, which is the default when pressing R then the axis you want once.